XIII-ÈME COLLOQUE FRANCO-ROUMAIN DE
MATHÉMATIQUES APPLIQUÉES
25-29 AOÛT 2016
FACULTE DE MATHEMATIQUES
UNIVERSITE „ALEXANDRU IOAN CUZA” DE IAȘI
SPONSORS
Les organisateurs remercient les institutions suivantes pour leur soutien financier à ce colloque:
ORGANISATEURS
Université Alexandru Ioan Cuza de Iași, România
Académie Roumaine, Institut „Octav Mayer”, Iași, România
Université de Bucarest, România
Académie Roumaine, Institute „Simion Stoilow”, Bucarest, România
Fundatia Seminarului Matematic „Al. Myller”
Université „Claude Bernard”, Lyon, France
Comité Scientifique
Lucian Beznea, Académie Roumaine, IMAR, Bucarest Didier Bresch, CNRS France
Nicolas Burq - Université Paris-Sud, Orsay Miguel Angel Fernández - INRIA, France Ioan R. Ionescu - Université Paris 13
Gabriela Kohr - Univ "Babeş-Bolyai", Cluj-Napoca Denis Talay – INRIA, France
Sanda Tigoiu – Université de Bucarest
Constantin Zălinescu - Université „Alexandru IoanCuza” de Iasi
Comité local d'organisation
Cătălin Lefter, [email protected] Marius Durea, [email protected] Marius Apetrii, [email protected]
Coordonateurs
Dragos Iftimie, Université Claude Bernard Lyon 1, France Petru Mironescu, Université Claude Bernard Lyon 1, France Radu Purice, IMAR Bucarest, România
Victor Tigoiu, Université de Bucarest, România
XIII-ÈME COLLOQUE FRANCO-ROUMAIN DE
MATHÉMATIQUES APPLIQUÉES
25-29 AOÛT 2016
FACULTE DE MATHEMATIQUES
UNIVERSITE „ALEXANDRU IOAN CUZA” DE IAȘI
TABLE DE MATIÈRES
Programme en bref 7
Programme 11
Résumés 31
Index 93
SESSIONS SPÉCIALES
Session 1: Nouvelles tendances en mécanique des fluides
Organisateurs
: Valentina Busuioc (Saint-Etienne), Franck Sueur (Bordeaux)Session 2: Problèmes à frontière libre
Organisateurs
: Vincent Duchène (Rennes), Eugen Varvaruca (Iasi)Session 3: Modèles mathèmatiques et méthodes numériques en mécanique des milieux continus
Organisateurs
: Mircea Sofonea (Perpignan), Cristian Faciu (Bucarest)Session 4: Processus stochastiques
Organisateurs
: Jean-Stephane Dhersin (Paris), Oana Lupaşcu (Bucarest), Titus Lupu (Zuerich)Session 5: Maths et planète Terre
Organisateurs
: Gabriela Marinoschi (Bucarest), Vuk Milisic (Paris)Session 6: Analyse et contrôle des EDP
Organisateurs
: Camille Laurent (Paris), Liviu Ignat (Bucarest), Sorin Micu (Craiova), Yannick Sire (Baltimore)Session 7: Statistiques
Organisateurs
: Céline Lacaux (Avignon), Cristian Preda (Lille et Bucarest)Session 8: Analyse non-lisse et optimisation
Organisateurs
: Abderrahim Jourani (Dijon), Nicolae Popovici (Cluj-Napoca), Michel Thera (Limoges)11
Programme
JEUDI, 25 AOÛT 2016
Ouverture Officielle
9:30 - 10:00 - Aula Magna Mihai Eminescu
CONFÉRENCES PLÉNIÈRES Aula Magna Mihai Eminescu 10:00-11:00
BARBU Viorel
„Alexandru Ioan Cuza” University of Iasi, Romania
Steepest descent algorithm in Wasserstein metric for the sandpile model 11:00-11:45
COCKTAIL DE BIENVENUE
Aula Magna Mihai Eminescu 11:45-12:45
CORON Jean - Michel
Université Pierre et Marie Curie, France Stabilization and nonlinearities
TRAVAUX DES SÉSSIONS
SESSION 2: PROBLÈMES À FRONTIÈRE LIBRE - Amf. P10 15:00-15:30
AMBROSE David Drexel University, USA
Traveling waves in interfacial fluid dynamics with multi-valued height
12
15:30-16:00 NILSSON Dag
Lund University, Sweden
Internal gravity-capillary solitary waves in finite depth 16:00-16:30
DE SILVA Daniela
Columbia University, USA The thin free boundary problem 16:30-17:00
PAUSE CAFÉ
17:00-17:30
VEGA SMIT Mariana
University of Duisburg-Essen, Germany
The obstacle problem for the fractional Laplacian with drift 17:30-18:00
VARHOLM Kristoffer
Norwegian University of Science and Technology, Norway
Global bifurcation of gravity water waves with multiple critical layers 18:00-18:30
WHEELER Miles
Courant Institute of Mathematical Sciences, USA Properties of solitary waves in deep water
SESSION 3: MODÈLES MATHÈMATIQUES ET MÉTHODES NUMÉRIQUES EN MÉCANIQUE DES MILIEUX CONTINUS - Amf. Al. Myller
15:00-15:30
MIGORSKI Stanislaw
Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, Poland Variational-Hemivariational Inequality in Contact Problem for Locking Materials
15:30-16:00 BADEA Lori
Institut de Mathématiques de l’Académie Roumaine, Roumanie
Méthode multigrille pour les inégalités contenant un terme non-différentiable 16:00-16:30
SOFONEA Mircea
University of Perpignan Via Domitia, France
Variational-Hemivariational Inequalities with Applications in Contact Mechanics
13
16:30-17:00 PAUSE CAFÉ 17:00-17:30 DUMONT Serge
UNimes/IMAG Montpellier, France
Active Set Method for solving Multi-Contact Problems 17:30-18:00
KALITA Piotr
Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, Poland Micropolar effects stabilize the flow for the Rayleigh-Bénard problem
18:00-18:30
PATRULESCU Flavius-Olimpiu
"Tiberiu Popoviciu" Institute of Numerical Analysis, Romanian Academy, Romania A regularization method for a viscoelastic contact problem
18:30-19:00 SLUZALEC Tomasz
Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, Poland Theoretical and numerical approach for problem solving steady-state heat conduction
SESSION 4: PROCESSUS STOCHASTIQUES - Salle de cours 2.1 15:00-16:00
DEACONU Mădălina
Inria Centre de Recherche Nancy - Grand Est & IECL, France
Stochastic approach of rupture phenomena - application to avalanches 16:00-16:30
LOPUSANSCHI Olga LPMA, Paris VI, France
Une construction de l’aire de Lévy avec drift comme limite renormalisée des chaînes de Markov sur graphes périodiques
16:30-17:00 PAUSE CAFÉ 17:00-18:00
VILLEMONAIS Denis
Université de Lorraine, France
Exponential convergence to a quasi-stationary distribution 18:00-19:00
MARZOUK Cyril
LPMA, Universités Paris VI et VII, France
Geometry of large random non-crossing partitions
14
SESSION 6: ANALYSE ET CONTRÔLE DES EDP - Amf. I.3 15:00-15:30
ROSIER Lionel
Mines ParisTech, France
Controllability of some evolution equations by the flatness approach 15:30-16:00
LISSY Pierre
CEREMADE, Université Paris-Dauphine, France The cost of fast controls for the heat equation 16:00-16:30
MARINOSCHI Gabriela
„Gheorghe Mihoc - Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Romania
Feedback stabilization of system for phase separation 16:30-17:00
PAUSE CAFÉ
17:00-17:30 ROVENTA Ionel
University of Craiova, Romania
Uniform boundary observability for finite differences discretisation of a clamped beam equation 17:30-18:00
CAZACU Cristian
Politehnica University of Bucharest and „Simion Stoilow” Institute of Mathematics, Romanian Academy, Romania
Controllability results for a Kuramoto-Sivashinsky model on trees 18:00-18:20
MUNTEANU Ionut
Bielefeld Universitat, Bielefeld, Germany Stabilization of parabolic-type equations 18:20-18:40
GRECU Andreea
"Simion Stoilow" Institute of Mathematics, Romanian Academy, Romania
Dispersive and Strichartz Estimates for the Solution of Schrodinger Equation on a Graph with Cycle 18:40-19:00
ZOUITEN Hayat
Moulay Ismail University, Faculty of Sciences, Meknes, Morocco
Enlarged Observability of the Gradient: A Numerical Approach
15
SESSION 8: ANALYSE NON-LISSE ET OPTIMISATION - Amf. II.6 15:00-15:30
NITICA Viorel
West Chester University of Pennsylvania, USA
Topological transitivity of extensions of hyperbolic systems 15:30-16:00
BONNEL Henri
University of New Caledonia and Curtin University, Perth, Australia and France Post Pareto Analysis for multiobjective parabolic control systems
16:00-16:30 BAGDASAR Ovidiu
University of Derby, United Kingdom
Extremal properties of explicitly quasiconvex vector functions
16:30-17:00 PAUSE CAFÉ
17:00-17:30 REVALSKI Julian
Bulgarian Academy of Sciences, Bulgaria
Uniform-like properties of the norm and optimization problems in Banach spaces 17:30-18:00
PINTEA Cornel
„Babeș-Bolyai” University, Cluj-Napoca, Romania
Global injectivity results for some classes of operators and applications 18:00-18:30
NICULESCU Constantin
University of Craiova, Romania
Old and new on 2d-increasing functions 18:30-19:00
GÜNTHER Christian
Martin Luther University Halle-Wittenberg, Institute for Mathematics, Germany Relationships between constrained and unconstrained multiobjective optimization 19:00-19:30
POPOVICI Nicolae
„Babeș-Bolyai” University, Cluj-Napoca, Romania
A decomposition approach to vector optimization and related variational problems
16
VENDREDI, 26 AOÛT 2016
CONFÉRENCES PLÉNIÈRES Amf. B1
8:30-9:30
TUCSNAK Marius
Université de Bordeaux, France
Control and identification for some infinite dimensional systems 9:30-10:30
SUEUR Franck
Institut de Mathématiques de Bordeaux, France On the controllability of the Navier-Stokes equations 10:30-11:00
PAUSE CAFÉ Amf. B1 11:00-12:00
NIKEGHBALI Ashkan Université de Zürich, Suisse
Ratios for the circular unitary ensemble and related problems for the Riemann zeta function 12:00-13:00
BUCUR Dorin
Université Savoie Mont Blanc, France Shape optimization of spectral functionals
TRAVAUX DES SÉSSIONS
SESSION 1: NOUVELLES TENDANCES EN MÉCANIQUE DES FLUIDES - Amf. II.4 15:00-15:30
BOSTAN Mihai
Aix-Marseille Université, Centre de Mathématiques et Informatique, France Multi-scale analysis for the Vlasov-Poisson equations
15:30-16:00 PIERRE Olivier
LMJL, University of Nantes, France
Analytic current-vortex sheets in incompressible magnetohydrodynamics 16:00-16:30
TRESCASES Ariane
University of Cambridge, UK
Régularité de l'équation de Boltzmann en domaine borné
17
16:30-17:00 PAUSE CAFÉ
17:00-17:30
KOLUMBAN Jozsef
Université Paris Dauphine, France
Control of the motion of a rigid body immersed in a perfect two-dimensional fluid 17:30-18:00
SCROBOGNA Stefano
University of Bordeaux, France
On fastly rotating and weakly compressible fluids 18:00-18:30
FANELLI Francesco
Institut Camille Jordan, Université Claude Bernard Lyon 1, France On some models of non-homogeneous inviscid fluids
SESSION 2: PROBLÈMES À FRONTIÈRE LIBRE - Amf. P10 15:00-15:30
CASTRO Angel
Universidad Autónoma de Marid and ICMAT, Spain Mixing solutions for the Muskat problem
15:30-16:00
GIANNOULIS Ioannis
University of Ioannina, Greece
Interaction of modulated gravity water waves of finite depth 16:00-16:30
PARAU Emilian
University of East Anglia, UK
Axisymmetric solitary waves on a ferrofluid jet
16:30-17:00 PAUSE CAFÉ 17:00-17:30
DE POYFERRÉ Thibault
Ecole Normale Supérieure, France
Dispersion and low regularity theory for capillary water waves 17:30-18:00
VELICHKOV Bozhidar
Université Grenoble Alpes, France
Regularity of the optimal sets for spectral functionals
18
18:00-18:30 CIOMAGA Adina
Universite Paris Diderot, France Homogenization of interfaces
SESSION 3: MODÈLES MATHÈMATIQUES ET MÉTHODES NUMÉRIQUES EN MÉCANIQUE DES MILIEUX CONTINUS - Amf. Al. Myller
15:00-15:30
CLEJA-TIGOIU Sanda, TIGOIU Victor University of Bucharest, Bucharest
Continuous model of structural defects in finite elasto-plasticity 15:30-16:00
IONESCU Ioan
Universtié Paris 13, Sorbonne Paris-Cité, France
Material instabilies in modeling multiscale anisotropic damage 16:00-16:30
CHIRIȚĂ Stan
„Alexandru Ioan Cuza” University of Iasi, Romania On the three-phase-lag model of heat conduction 16:30-17:00
PAUSE CAFÉ
17:00-17:30
CRACIUN Eduard - Marius
"Ovidius" University of Constanta, Romania
Mathematical Modeling of Interface Cracks in Fiber Reinforced Elastic Composites 17:30-18:00
GHIBA Ionel-Dumitrel
„Alexandru Ioan Cuza” University of Iasi and University of Duisburg-Essen, Romania and Germany On some Hencky-type energies
18:00-18:30 GARAJEU Mihail
Université Aix-Marseille, France
Solutions exactes d’une sphère composite viscoélastique non linéaire sous chargement isotrope 18:30-19:00
NECIB Brahim
University of Constantine, Algeria
Analyse dynamique des structures bidimensionnelles planes par modélisation continue utilisant la
méthode des éléments finis
19
SESSION 4: PROCESSUS STOCHASTIQUES - Salle de cours 2.1 15:00-16:00
GOREAC Dan
Université Paris-Est, UMR8050, France
Control-Based Design for Stochastic Gene Networks 16:00-16:30
MATICIUC Lucian
"Gheorghe Asachi" Technical University, Iasi, Romania
A Generalized Skorokhod Problem with Càdlàg Discontinuities
16:30-17:00 PAUSE CAFÉ 17:00-18:00 PASCU Mihai
„Transilvania” University of Brasov, Romania
Brownian couplings on constant curvature manifolds 18:00-18:30
ZALINESCU Adrian
"Octav Mayer" Institute of Mathematics, Romanian Academy, Iasi, Romania Jump diffusions with oblique subgradients
18:30-19:00 CIMPEAN Iulian
„Simion Stoilow” Institute of Mathematics, Romanian Academy, Romania From excessive functions to semimartingales on Dirichlet spaces
SESSION 5: MATHS ET PLANÈTE TERRE - Faculty Conference Room
14:30-15:00
CHOQUET Catherine
Laboratoire MIA, Université de La Rochelle, France
New approach for the tracking of fluid displacement in stratified flows 15:00-15:30
DIMITRIU Gabriel
"Grigore T. Popa" University of Medicine and Pharmacy Iasi, Romania Data assimilation using low-rank Kalman filtering
15:30-16:00 PETCU Mădălina
University of Poitiers, France
Etude théorique et numérique sur les équations Cahn-Hilliard-Navier-Stokes visqueuses avec des
conditions aux bords dynamiques
20
16:00-16:30
CRUCEANU Ștefan-Gicu
"Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of Romanian Academy, Romania
Riemann Problem for Shallow Water Equations with Discontinuous Porosity
16:30-17:00 PAUSE CAFÉ
17:00-17:30 BUONOMO Bruno
Federico II University of Naples, Italy
Modelling the effects of malaria infection on mosquito biting behaviour and attractiveness of humans
17:30-18:00 ANIȚA Sebastian
„Alexandru Ioan Cuza” University of Iasi, Romania
Regional control for some spatially structured populations 18:00-18:30
BOUIN Emeric
CEREMADE, Université Paris-Dauphine, France Propagation in structured models from biology 18:30-19:00
GEORGESCU Paul
„Gheorghe Asachi” Technical University of Iasi, Romania On a HIV transmission model with two high risk groups
SESSION 6: ANALYSE ET CONTRÔLE DES EDP - Amf. I.3
15:00-15:30 LAURENT Camille
Université Pierre et Marie Curie, France
Quantitative unique continuation, intensity of waves in the shadow of obstacle and approximate control
15:30-16:00 PIRVU Traian
McMaster University, Canada
On a Stochastic Control Problem with Regime Switching
21
16:00-16:30
GAGNON Ludovick
Université Pierre et Marie Curie, France Rapid Stabilization of a Schrödinger Equation 16:30-17:00
PAUSE CAFÉ 17:00-17:30 LIARD Thibault
Laboratoire Jacques Louis Lions, Université Pierre et Marie Curie, France
A Kalman rank condition for the indirect controllability of coupled systems of linear operator groups 17:30-18:00
MOYANO Ivan
CMLS, Ecole Polytechnique, France
Local exact controllability of a quantum particle in a time-varying 2D disc with radial data 18:00-18:20
VIOREL Adrian
Technical University of Cluj-Napoca, Romania Metastability for the Radiative Gas Model 18:20-18:40
SAAOF Abdel-Ilah
Faculty of Sciences, Moulay Ismail University, Meknes, Morocco Boundary constrained observability for hyperbolic systems 18:40-19:00
TOREBEK Berikbol
Institute of Mathematics and Mathematical Modeling, Kazakhstan
Green function of the Robin and Steklov problems for the Laplace operator
SESSION 7: STATISTIQUES - Salle de cours 2.6 15:00-15:30
CIUPERCA Gabriela Université Lyon 1, France
Détections de changements dans un modèle paramétrique 15:30-16:00
MONTUELLE Lucie
Université Paris Diderot, France Short-term wind power forecasting 16:00-16:30
ROBE-VOINEA Elena-Grațiela University of Bucharest, Romania
Multivariate aggregate claims evaluation using the Fast Fourier Transform
22
16:30-17:00 PAUSE CAFÉ
SESSION 8: ANALYSE NON-LISSE ET OPTIMISATION - Amf. II.6
15:00-15:30 COSTEA Nicușor
Politehnica University and „Simion Stoilow” Institute of Mathematics, Romanian Academy, Bucharest, Romania
Bounded saddle point methods for locally Lipschitz functionals 15:30-16:00
PREDA Vasile, NICULESCU Cristian University of Bucharest, Romania
Hölder Continuity of Solutions of Generalized Ky Fan Inequalities 16:00-16:30
LÁSZLÓ Szilárd
Technical University of Cluj-Napoca, Romania Minimax results on dense sets
16:30-17:00 PAUSE CAFÉ
17:00-17:30 PATRICHE Monica
University of Bucharest, Romania
Existence of equilibrium for generalized games in choice form and applications 17:30-18:00
ZAGRODNY Dariusz
Cardinal Stefan Wyszyński University, Poland
Regularity and Lipschitz-like properties of subdifferential 18:00-18:30
GRAD Anca
„Babeș-Bolyai” University of Cluj-Napoca, Romania Optimiality conditions by means of generalized interiors 18:30-19:00
THERA Michel
University of Limoges, France
An overview on the implicit (multifunction) theorem from I. Newton to nowadays
23
SAMEDI, 27 AOÛT 2016
CONFÉRENCES PLÉNIÈRES Amf. B1
8:30-9:30
ZĂRNESCU Arghir
Basque Center for Applied Mathematics and "Simion Stoilow" Institute of Mathematics, Romanian Academy, Spain and Romania
Anisotropic features in liquid crystal models 9:30-10:30
MACIA Fabricio
Universidad Politecnica de Madrid, Spain
Dispersion and controllability for linear Schrödinger equations
10:30-11:00 PAUSE CAFÉ
Amf. B1 11:00-12:00
RAUGEL Geneviève
CNRS et Université Paris-Sud, France
Dynamics of the damped focusing subcritical Klein-Gordon equation 12:00-13:00
POPESCU Ionel
Georgia Institute of Technology and "Simion Stoilow" Institute of Mathematics, Romanian Academy, USA and Romania
Inequalities in Free Probability on the circle TRAVAUX DES SÉSSIONS
SESSION 1: NOUVELLES TENDANCES EN MÉCANIQUE DES FLUIDES - Amf. II.4
15:00-15:30 MIOT Evelyne
CNRS, Université Grenoble Alpes, France
On the convergence of the Vlasov-Poisson system to the Euler equation in the gyrokinetic limit 15:30-16:00
MONNIAUX Sylvie
Université Aix-Marseille, France
The Dirichlet-to-Neumann problem associated with the Stokes operator
24
16:00-16:30
CIUPERCA Sorin Ionel
Institut Camille Jordan, Université Claude Bernard Lyon 1, France
Existence et unicité d'une solution densité de probabilités pour une équation de Doi-Edwards stationnaire
16:30-17:00 PAUSE CAFÉ
17:00-17:30 IFTIMIE Dragoș
Université Lyon 1, France
Self-similar point vortices and confinement of vorticity 17:30-18:00
BURTEA Cosmin
Université Paris-Est Créteil, France
New long time existence results for a class of Boussinesq-type systems 18:00-18:30
LEFTER Cătălin-George
„Alexandru Ioan Cuza” University of Iași, Romania
Boundary stabilization of fluid dynamics. An operatorial approach
SESSION 3: MODÈLES MATHÈMATIQUES ET MÉTHODES NUMÉRIQUES EN MÉCANIQUE DES MILIEUX CONTINUS - Amf. Al. Myller
15:00-15:30
DANESCU Alexandre
École Centrale de Lyon, France
Mindlin model as an exact interpolation of the chain with hyper-pre-stress 15:30-16:00
GALEȘ Cătălin
„Alexandru Ioan Cuza” University of Iasi, Romania Resonance effects in the dynamics of space debris 16:00-16:30
MALIN Maria
City University of Hong Kong, China
Nonlinear Korn inequalities on a surface: some new results 16:30-17:00
PAUSE CAFÉ
25
17:00-17:30 PASA Gelu
„Simion Stoilow” Institute of Mathematics, Romanian Academy, Romania On the 3D immiscible displacement in Hele-Shaw cells
17:30-18:00
BUCUR Andreea-Valentina
„Alexandru Ioan Cuza” University of Iasi, Romania
Spatial behavior in linear theory of thermoviscoelasticity backward in time for porous media 18:00-18:30
FACIU Cristian
„Simion Stoilow” Institute of Mathematics, Romanian Academy, Romania Modeling temporal and spatial instabilities of the Portevin - Le Chatelier effect
SESSION 4: PROCESSUS STOCHASTIQUES - Salle de cours 2.1
15:00-16:00 RĂȘCANU Aurel
”Octav Mayer” Institute of Mathematics, Romanian Academy, Romania On the continuity of the Feynman-Kac formula
16:00-16:30
ROTENSTEIN Eduard
"Alexandru Ioan Cuza" University of Iasi, Romania
Infection Time in Multi-Stable Gene Networks. A BSVI With Non-Convex, Switch-Dependent Reflection Model
16:30-17:00 PAUSE CAFÉ
17:00-17:30
GROSU Alexandra Claudia
„Alexandru Ioan Cuza” University of Iasi, Romania
Approximate (null-)controllability; Controlled Markov switch process; Invariance; Stochastic gene networks
17:30-18:00 LAZARI Alexandru
Moldova State University, Republic of Moldova
Stationary Stochastic Games with Final Sequence of States
26
SESSION 5: MATHS ET PLANÈTE TERRE - Faculty Conference Room
15:00-15:30 BEZNEA Lucian
„Simion Stoilow” Institute of Mathematics, Romanian Academy and University of Bucharest, Romania Branching processes associated with Neumann nonlinear semi flows
15:30-16:00 GABRIEL Pierre
Université de Versailles, France
A Hamilton-Jacobi equation for subdiffusive motion 16:00-16:30
LUPASCU Oana
„Simion Stoilow” Institute of Mathematics, Romanian Academy, Romania Branching properties for measure-valued Markov process and applications 16:30-17:00
PAUSE CAFÉ
17:00-17:30 HALANAY Andrei
Politehnica University of Bucharest, Romania
A complex model for cell evolution in hematological diseases incorporating treatment, competition and the action of the immune system
17:30-18:00 LITCANU Gabriela
"Octav Mayer" Institute of Mathematics Iasi, Romanian Academy, Romania Mathematical modelling of the immune response
18:00-18:30 BADRALEXI Irina
Politehnica University of Bucharest, Romania Periodic solutions in a DDE model
SESSION 6: ANALYSE ET CONTRÔLE DES EDP - Amf. I.3
15:00-16:00 SAVIN Ovidiu
Columbia University, USA
Obstacle type problems for minimal surfaces
27
16:00-16:30
MARICA Aurora-Mihaela
Politehnica University of Bucharest, Romania Wave propagation on irregular grids
16:30-17:00 PAUSE CAFÉ
17:00-17:20
IAGAR Răzvan Gabriel
Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain Finite time extinction for diffusive Hamilton-Jacobi equations 17:20-17:40
MIHĂILESCU Mihai
University of Craiova and "Simion Stoilow" Institute of Mathematics, Romanian Academy, Romania Classification of isolated singularities for inhomogeneous operators in divergence form
17:40-18:00
STANCU-DUMITRU Denisa
Politehnica University of Bucharest and "Simion Stoilow" Institute of Mathematics, Romanian Academy, Bucharest, Romania
A perturbed eigenvalue problem on general domains 18:00-18:20
STANCUT Ionela - Loredana University of Craiova, Romania
Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces 18:20-18:40
FARCASEANU Maria
University of Craiova and "Simion Stoilow" Institute of Mathematics, Romanian Academy, Romania On the convergence of the sequence of solutions for a family of eigenvalue problems
18:40-19:00
BIROUD Kheireddine
Ecole préparatoire d'économie de Tlemcen, Algéria
Existence and nonexistence for semilinear problem with sigular term 19:00-19:20
MARDARE Sorin
Université de Rouen, France
Analyse asymptotique du problème de Neumann dans de longs cylindres
28
SESSION 7: STATISTIQUES - Salle de cours 2.6 15:00-15:30
TOMA Aida
Academy of Economic Studies, Bucharest, Romania
Minimum dual divergence estimators for moment condition models 15:30-16:00
DEDU Silvia
University of Economic Studies, Bucharest, Romania
Weighted power type probability distributions. Statistical properties and applications 16:00-16:30
ROCHE Angelina
Université Paris Dauphine, France
Kernel adaptive estimation for functional data
16:30-17:00 PAUSE CAFÉ
SESSION 8: ANALYSE NON-LISSE ET OPTIMISATION - Amf. II.6
15:00-15:30 SEREA Oana Silvia
Université Perpignan Via Domitia, France
On control problems associated with sweeping processes 15:30-16:00
FLORESCU Liviu
„Alexandru Ioan Cuza” University of Iasi, Romania Sur la continuité des fonctionnelles intégrales 16:00-16:30
VILCHES Emilio
University of Burgundy and University of Chile, France and Chile On a generalized perturbed sweeping process with nonregular sets 16:30-17:00
PAUSE CAFÉ 17:00-17:30
KHANH Phan Quoc
Vietnam National University Ho Chi Minh City, International University, Vietnam
Variational convergence of bifunctions on nonrectangular domains and approximations of
quasivariational problems
29
17:30-18:00 NECOARA Ion
Politehnica University Bucharest, Romania
Linear convergence of gradient type methods for non-strongly convex optimization 18:00-18:30
JOURANI Abderrahim
Université de Bourgogne Franche-Comté, France Favorable classes for radiality and semismoothness 18:30-19:00
STRUGARIU Radu
„Gheorghe Asachi” Technical University of Iasi, Romania
A new type of directional regularity for multifunctions with applications to optimization
DIMANCHE, 28 AOÛT 2016
CONFÉRENCES PLÉNIÈRES Amf. B1
8:30-9:30 MARIN Liviu
University of Bucharest and Institute of Solid Mechanics, Romanian Academy, Romania Efficient and stable algorithms for direct and inverse problems in thermoelasticity 9:30-10:30
PAGÈS Gilles
Université Pierre et Marie Curie, France
Weighted Multilevel estimator: from Ulahm to Langevin Monte Carlo simulation 10:30-11:00
PAUSE CAFÉ
Amf. B1 11:00-12:00 KOHR Mirela
„Babeș-Bolyai” University, Cluj-Napoca, Romania
Boundary value problems for nonlinear Brinkman and Navier-Stokes equations with variable coefficients in Lipschitz domains
12:00-13:00 DUREA Marius
"Alexandru Ioan Cuza" University, Iasi, Romania
Regularities and subregularities with respect to fixed sets and applications
R´ ESUM´ ES
Conf´ erences pl´ eni` eres
Steepest descent algorithm in Wasserstein metric for the sandpile model
BARBU Viorel
“Alexandru Ioan Cuza” University of Ia¸si, Romania
It is established the convergence in Wasserstein metric of steepest algorithm for the nonlinear diffusion equation describing the self-organized sand pile model.
Shape optimization of spectral functionals
BUCUR Dorin, GIACOMINI A.
Universit´e Savoie Mont Blanc, France
Motivated by spectral optimization problems, we provide a free discontinuity approach to a class of shape optimization problems involving Robin conditions on the free boundary. More precisely, we identify a large family of domains on which such problems are well posed in a way that the extended problem can be considered a relaxed version of the corresponding one on regular domains, we prove existence of a solution and obtain some qualitative information on the optimal sets.
33
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Conf´erences pl´eni`eres
Stabilization and nonlinearities
CORON Jean-Michel
Universit´e Pierre et Marie Curie, France
A control system is a dynamical system on which one can act by using controls. For these systems a fun- damental problem is the stabilization issue: is it possible to stabilize a given unstable equilibrium by using suitable control laws? (Think to the classical experiment of an upturned broomstick on the tip of one’s finger.) We first present some pioneer devices and works (Ktesibios, Watt, Foucault, Maxwell, Lyapunov...) and then some recent results. A special emphasis is put on the importance of the nonlinearities for the stabilization issue and an application to the regulation of the rivers La Sambre and La Meuse is presented.
Regularities and subregularities with respect to fixed sets and applications
DUREA Marius
“Alexandru Ioan Cuza” University of Iasi, Romania
Motivated by some known fixed point results, we introduce several regularities with respect to sets for mappings. We underline the importance of parametric subregularity property of set-valued mappings, defined with respect to fixed sets, in order to get some important applications. We show that this property appears naturally for very simple mappings which play an important role in the theory of metric regularity. We prove a result concerning the preservation of metric subregularity at generalized compositions. Then we obtain, in purely metric setting, several fixed point assertions for set-valued mappings in local and global frameworks.
Boundary value problems for nonlinear Brinkman and
Navier-Stokes equations with variable coefficients in Lipschitz domains
KOHR Mirela, De CRISTOFORIS LANZA Massimo, MIKHAILOV Sergey E., and WENDLAND Wolfgang L.
Faculty of Mathematics and Computer Science, Babe¸s-Bolyai University, Cluj-Napoca, Romania
In this talk we present recent existence and uniqueness results in Sobolev and Besov spaces for boundary value problems involving nonlinear Brinkman and Navier-Stokes systems with constant/variable coefficients
34
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Conf´erences pl´eni`eres
in Lipschitz domains in Euclidean setting or in compact Riemannian manifolds. Such problems have various applications in fluid mechanics and porous media. We use layer potential theoretic methods combined with fixed point theorems to show the desired existence and uniqueness results.
Dispersion and controllability for linear Schr¨ odinger equations
MACIA Fabricio, ANANTHARAMAN Nalini, and LEAUTAUD Matthieu
Universidad Politecnica de Madrid, Spain
We present some results concerning internal and boundary controllability for linear Schr¨odinger equations.
We are interested in situations in which the underlying geometry is completely integrable. This means that, when the equation is posed on a domain of euclidean space (resp. on a manifold), the billiard dynamical system on the domain (resp. the geodesic flow) is completely integrable. This is the case if the domain is a disk on the plane; another important example is the periodic Schr¨odinger equation (which corresponds to a torus).
We give necessary and sufficient conditions for controllability. Our methods of proof are based on a careful analysis of dispersive properties of solutions to the equation with respect to transverse directions to certain invariant tori for the billiard/geodesic flow dynamics.
Efficient and stable algorithms for direct and inverse problems in thermoelasticity
MARIN Liviu, JOHANSSON B. Tomas, KARAGEORGHIS Andreas, and LESNIC Daniel
University of Bucharest & Institute of Solid Mechanics of the Romanian Academy, Romania
We propose efficient FFT-based algorithms for the numerical solution of certain problems in planar ther- moelasticity, as well as accurate, convergent and stable regularization algorithms for some inverse boundary value problems in two- and three-dimensional thermoelasticity.
35
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Conf´erences pl´eni`eres
Ratios for the circular unitary ensemble and related problems for the Riemann zeta function
NIKEGHBALI Ashkan
Universit´e de Z¨urich, Suisse
We show that after proper scalings, the characteristic polynomial of a random unitary matrix converges almost surely to a random analytic function whose zeros, which are on the real line, form a determinantal point process with sine kernel. As an application, we give a solution to the problem of convergence of ratios of characteristic polynomials at the microscopic scale and we conjecture some new limit theorems for the value distribution of the Riemann zeta function on the critical line at the stochastic process level.
Weighted Multilevel estimator: from Ulahm to Langevin Monte Carlo simulation
PAG` ES Gilles
UPMC, France
We propose and analyze a Multilevel Richardson-Romberg (ML2R) estimator which combines the higher order bias cancellation of the Multistep Richardson-Romberg extrapolation introduced in [Pag`es 07] and the variance control resulting from the stratification in the Multilevel Monte Carlo (MLMC) method (see [Giles
’08]). TheML2R estimator appears as a weighted version of the MLMC, with universal weights.
In standard frameworks like discretization schemes of diffusion processes, an assigned quadratic error epsilon can be obtained using the ML2R estimator with a global complexity of log(1/ε)ε(−2) instead of (log(1/ε))2ε(−2) with the standard MLMC method, at least when the weak discretization error associated to (functionals of) the scheme can be expanded at any order in the step Tn and the quadratic (strong) error behaves likeOq
T n
. This is half-way betweenMLMCand a virtual unbiased simulation. More generally, the slower the quadratic strong error the goes to 0, the higher the complexity reduction is.
We analyze and compare these estimators on several numerical problems: option pricing (vanilla or exotic) using Monte Carlo simulation and the less classical Nested Monte Carlo simulation (see [Gordy & Juneja 2010]).
In a second step, we adapt similar ideas to Langevin Monte Carlo simulation for the recursive computation of invariant distributions of diffusions with applications to stationary stochastic volatility models.
36
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Conf´erences pl´eni`eres
Inequalities in Free Probability on the circle
POPESCU Ionel
Georgia Institute of Technology & IMAR, USA & Romania
In this talk we will describe a few inequalities in free probability on the circle and reveal some interesting questions they inspire in the classical counterpart.
Dynamics of the damped focusing subcritical Klein-Gordon equation
RAUGEL Genevieve, BURK N., and SCHLAG W.
CNRS et Universit´e Paris-Sud, France
We consider the focusing subcritical Klein-Gordon equation with constant positive damping and radial data.
In particular, we show that either the solutions blow up in finite time or they converge to an equilibrium point.
On the controllability of the Navier-Stokes equations
SUEUR Franck
Institut de Math´ematiques de Bordeaux, France
We will describe some results regarding the controllability of the Navier-Stokes equations from one part of the boundary. The issue is to drive the system from a given initial state to a wished final state in a given time interval thanks to some appropriate boundary conditions on the controlled part of the boundary. We will examine in particular the difficulties related to boundary layers near the uncontrolled part of the boundary.
37
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Conf´erences pl´eni`eres
Control and identification for some infinite dimensional systems
TUCSNAK Marius
Universit´e de Bordeaux, France
The physical problem motivating this work is the motion of a piston in a cylinder filled with some gas. This is a free boundary problem which received a considerable attention within the last decades. We examine a hierarchy of models, from a toy one to a much more realistic one.
In the toy problem the fluid is modeled by the viscous Burgers equation. In this case we prove well- posedness, stabilization and controllability results. The next model assumes that the fluid is governed by the 1Dcompressible Navier-Stokes problem. We prove global existence and uniqueness for non homogeneous boundary data. Finally, we study a system modelling the motion of a piston in a cylinder filled by a viscous heat conducting gas. The piston is moving longitudinally without friction under the influence of the forces exerted by the gas. The fact that the piston is supposed be thermally insulating (adiabatic piston) raises several challenges which received a considerable attention, essentially in the statistical physics literature. We consider a model based on the Navier-Stokes-Fourier equations in one space dimension for the gas coupled with Newton’s law for the piston. Our main results assert the global in time existence of strong solutions and that the state trajectories converge to an equilibrium state when t→ ∞.
Anisotropic features in liquid crystal models
ZARNESCU Arghir
Basque Center for Applied Mathematics and “Simion Stoilow” Institute, Spain and Romania
The specific mathematical feature of liquid crystal models is that one works with functions taking values into certain manifolds. The physical and material symmetries then impose restrictions on the types of spatial variations allowed in the energy functionals. Apart from the usual Dirichlet energy there are certain combi- nations of first order derivatives, that generate in the corresponding Euler-Lagrange equations matrix-valued elliptic operators that are far from being diagonal.
38
Session 1
Nouvelles tendances en m´ ecanique des fluides
Organisateurs:
Valentina Busuioc (Saint-Etienne) Franck Sueur (Bordeaux)
Multi-scale analysis for the Vlasov-Poisson equations
BOSTAN Mihai
Aix-Marseille Universit´e - Centre de Math´ematiques et Informatique, France
We perform the mathematical analysis for the Vlasov-Poisson equations, in the magnetic confinement setting (large magnetic field). We justify the convergence toward the limit model, and investigate its main proper- ties. The arguments rely on two-scale analysis combined to ergodic theory (average operators along unitary groups).
New long time existence results for a class of Boussinesq-type systems
BURTEA Cosmin
Universit´e Paris-Est Cr´eteil, France
In this talk we deal with the long time existence for the Cauchy problem associated to some asymptotic models for long wave, small amplitude gravity surface water waves. We generalize some of the results that can be found in the literature devoted to the study of Boussinesq systems by implementing an energy method on spectrally localized equations. In particular, we obtain better results in terms of the regularity level required to solve the initial value problem on large time scales and we do not make use of the positive depth assumption.
39
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Session 1: Nouvelles tendances en m´ecanique des fluides
Existence et unicit´ e d’une solution densit´ e de probabilit´ es pour une ´ equation de Doi-Edwards stationnaire
CIUPERCA Sorin Ionel
Institut Camille Jordan, Universit´e Claude Bernard Lyon 1, France
Le mod`ele de Doi-Edwards est bas´e sur la th´eorie cin´etique et d´ecrit la distribution des mol´ecules dans un polym`ere fondu. Chaque mol´ecule est repr´esent´e pour une courbe dans l’espace, appell´ee chaine primitive et nous consid´erons une distribution de ces mol´ecules selon deux variables dites microscopique:s∈[0,1] et u∈S2 qui repr´esentent respectivement une coordonn´ee courviligne normalis´ee et l’orientation dans l’espace (iciS2est la sph`ere unite dansR3). Dans sa variante stationnaire, l’´equation de Doi-Edwards s’´ecrit: trouver F =F(s, u) (qui est la densit´e de distribution des mol´ecules) telle que
(−∂∂s2F2 +∂u∂ (GF)−αF ku·u+α∂s∂ [F k:λ(F)] = 0 F(s= 0) =F(s= 1) = 4π1 .
Dans cette ´equationα≥0 est un param`etre physique,k∈ M3(R) est le gradient de vitesse du fluide, suppos´e connu,G=ku−ku·uuet
λ(F)(s) = Z s
0
Z
S2
F(s0, u)u⊗u du ds0.
Nous montrons, pour α“proche” de 0, l’existence et l’unicit´e d’une solution d’´equation et le fait que cette solution est une densit´e de probabilit´e enu.
On some models of non-homogeneous inviscid fluids
FANELLI Francesco
Institut Camille Jordan, Universit´e Claude Bernard Lyon 1, France
In this talk we review recent results on strong solutions theory for some models of inviscid fluids with variable density. In the first part we will be concerned with the well-posedness of Euler equations in critical spaces, and with the propagation of geometric structures related to the vortex patch configuration. In the second part, we will turn the attention to a zero-Mach number system, derived by Alazard from the incompressible limit of the full compressible Euler equations. After making a connection with other quasi-incompressible models, and with the problem of propagation of interfaces, we will study its well-posedness in critical spaces.
40
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Session 1: Nouvelles tendances en m´ecanique des fluides
Self-similar point vortices and confinement of vorticity
IFTIMIE Dragos, MARCHIORO Carlo
Universit´e Lyon 1, France
We discuss several issues on the large time behavior of solutions of the incompressible Euler equations in dimension two. The point-vortex system, a discrete version of the Euler equations, gives a good indication on what this large time behavior should be. Of particular interest are the so-called self-similar configurations of point vortices which either collapse to a point or, when reversing time, grow to infinity like the square root of the time. We consider such a self-similar configuration of point vortices and we find a condition on the point vortices such that a vorticity initially confined around one point vortex will remain confined around the point vortex. We will also discuss its relevance to the large time behavior of the Euler equations.
Control of the motion of a rigid body immersed in a perfect two-dimensional fluid
KOLUMBAN Jozsef
Universit´e Paris Dauphine, France
We consider the motion of a rigid body immersed in a two-dimensional irrotational perfect fluid. The fluid is assumed to be confined in a bounded domain. We achieve exact controllability of the solid by using impulsive boundary control on the fluid. We treat separately the case when there is no circulation around the solid, then we extend our controllability result to the case with circulation using topological and time-rescale arguments.
Boundary stabilization of fluid dynamics. An operatorial approach
LEFTER C˘ at˘ alin-George
“Alexandru Ioan Cuza” University of Iasi, Romania
We intend to present an operatorial approach to the problem of boundary stabilization and control of Navier- Stokes type equations. We analyze the observability inequalities corresponding to various situations for the boundary control, entering the equation through non-slip (Dirichlet) or slip type (Navier) boundary condi- tions.
41
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Session 1: Nouvelles tendances en m´ecanique des fluides
On the convergence of the Vlasov-Poisson system to the Euler equation in the gyrokinetic limit
MIOT Evelyne
CNRS - Universit´e Grenoble Alpes, France
We investigate the gyrokinetic limit for the Vlasov-Poisson equation in two dimensions. In an appropriate asymptotic regime, we extend a result by L. Saint-Raymond on the convergence of the solutions towards a weak vorticity solution of the 2D Euler equation.
The Dirichlet-to-Neumann problem associated with the Stokes operator
MONNIAUX Sylvie
Universit´e Aix-Marseille, France
On a bounded strongly Lipschitz domain, we define the Stokes operators associated with homogeneous Dirich- let and Neumann boundary conditions in the spaceL2. Using the Dirichlet-to-Neumann operator associated with the Stokes operator, we prove that their eigenvalues compare the same way the eigenvalues of the Lapla- cian with homogeneous Dirichlet and Neumann boundary conditions compare, as in Friedlander’s result.
Analytic current-vortex sheets in incompressible magnetohydrodynamics
PIERRE Olivier
LMJL, University of Nantes, France
Current-vortex sheets are a particular tangential discontinuity in magnetohydrodynamics (MHD). This is a well-known problem since the 1950’s: it models the coupling between two plasmas separated by a free surfaceΓ(t) (tis the time variable), which give rise to a tangential discontinuity acrossΓ(t). More precisely,
“vortices” are created around the free surface Γ(t) because of the jumps of the tangential velocity and the tangential magnetic field. The free surface is thus calledcurrent-vortex sheet.
We will show how to construct analytic solutions to the current-vortex sheet problem, using a Cauchy- Kowalevskaya theorem. To do so, we begin with reducing the problem into afixeddomain in a suitable way, as is common for free boundary problems. Afterwards, we introduce some Banach spaces of analytic functions, satisfying crucial differentiation and algebra properties. Such Banach spaces will allow us to compute analytic estimates associated with thefront of the discontinuity and the so-calledtotal pressure in order to conclude with a Cauchy-Kowalevskaya theorem.
42
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Session 1: Nouvelles tendances en m´ecanique des fluides
On fastly rotating and weakly compressible fluids
SCROBOGNA Stefano, NGO Van-Sang
University of Bordeaux, France
This exposition is focused on the dynamics of inviscible, fastly rotating and slightly barotropic hydrody- namical flows. In the regime in which Rossby number and Mach numbers tend to zero at the same rate there are present two-types of dispersive effect, due respectively to high-speed propagation of acoustic waves and centrifugal effects, these effects can be studied combined via Strickartz estimates. We prove that these pertubations, although they propagate at a speed, converge strongly to zero in some appropriate space. This allows us to prove that the limit hydrodynamic flow is globally well posed in for although it is a 3D flow.
R´ egularit´ e de l’´ equation de Boltzmann en domaine born´ e
TRESCASES Ariane
University of Cambridge, UK
L’´equation de Boltzmann mod´elise l’´evolution de la densit´e de particules d’un gaz rar´efi´e. En domaine born´e (avec r´eflexion diffusive au bord), la solution pr´esente un comportement singulier sur les trajectoires rasant le bord du domaine. Dans le cas dun domaine convexe, les singularit´es sont confin´ees au bord rasant, alors que dans le cas d’un domaine non-convexe, certaines trajectoires singuli`eres p´en`etrent le domaine et des discontinuit´es peuvent se propager `a`a l’int´erieur. Nous ´etudions la question de la r´egularit´e de la solution dans les deux cas.
43
Session 2
Probl` emes ` a fronti` ere libre
Organisateurs:
Vincent Duchne (Rennes) Eugen V˘arv˘aruc˘a (Ia¸si)
Traveling waves in interfacial fluid dynamics with multi-valued height
AMBROSE David
Drexel University, USA
We present a formulation for traveling waves in interfacial fluid dynamics which allows for waves with multi- valued height. For 2D flows with surface tension, we use this formulation to prove a global bifurcation theorem.
We illustrate this theorem with detailed numerical simulations, which show that all of the predicted terminal behaviors from the global bifurcation theorem can indeed occur. These behaviors include the reconnection of the bifurcation curve to a trivial state, which is a phenomenon typically proved impossible for pure gravity water waves.
Mixing solutions for the Muskat problem
CASTRO Angel
Universidad Aut´onoma de Marid and ICMAT, Spain
We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type H5 initial data in the fully unstable regime.
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XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Session 2: Probl`emes `a fronti`ere libre
Homogenization of interfaces
CIOMAGA Adina
Universit´e Paris Diderot, France
We will present recent results on homogenization of interfaces, in stationary ergodic environments. These prob- lems can be reformulated, using the levelset method, as homogenizations problems for Hamilton-Jacobi equa- tions with non-coercive Hamiltonians. We extend the results obtained in the periodic setting by Cardaliaguet, Lions and Souganidis (2009) and show that although the interfaces may break, there is weak convergence of solutions, determined by the properties of the random media.
Dispersion and low regularity theory for capillary water waves
DE POYFERR´ E Thibault, NGUYEN Quang Huy
Ecole Normale Sup´erieure, France
The capillary water waves equation describes the motion of a liquid surface subject to surface tension, a dispersive physical phenomenon. A mathematical consequence of this dispersion is the family of Strichartz estimates. We present a work in which we prove those estimates at low regularity and use them to solve the Cauchy problem at low regularity, corresponding to a non-Lipschitz velocity field.
The thin free boundary problem
DE SILVA Daniela
Columbia University, USA
We present an overview of regularity results for the so-called thin one-phase free boundary problem intro- duced by Caffarelli-Roquejoffre-Sire as a model of a “non-local” Bernoulli problem. The starting point is the regularity theory for the classical Bernoulli problem, first investigated by Alt-Caffarelli. We also discuss some connections with other thin obstacle-type free boundary problems.
46
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Session 2: Probl`emes `a fronti`ere libre
Interaction of modulated gravity water waves of finite depth
GIANNOULIS Ioannis
University of Ioannina, Greece
Starting from the Zakharov/Craig-Sulem formulation for the water waves problem of finite depth with and without surface tension (capillary-gravity and gravity waves, respectively), we are interested in the macro- scopic manifestation of the interaction of different weakly amplitude-modulated plane waves of the linearized problem when amplitude, macroscopic space and macroscopic time have the same scaling coefficient. Apart from the formal derivation of the corresponding modulation equations, we present results concerning their justification in the case of gravity waves, which are based on recent work of Alvarez-Samaniego and Lannes on the long-time well-posedness of the water waves problem of finite depth.
Internal gravity-capillary solitary waves in finite depth
NILSSON Dag
Lund University, Sweden
Internal waves are waves which propagate along the interface of two fluids of different density. In this talk, I will present some new results regarding existence of internal solitary waves under the influence of gravity and surface tension. The main idea is to use a spatial dynamics approach and formulate the steady Euler equations as an evolution equation. This equation is then studied by using the center manifold theorem.
These techniques have previously been applied successfully to the surface wave case.
Axisymmetric solitary waves on a ferrofluid jet
PARAU Emilian
University of East Anglia, UK
Travelling axisymmetric solitary waves on the surface of a cylindrical ferrofluid jet are investigated. An azimuthal magnetic field is generated by an electric current flowing along a stationary metal rod which is mounted along the axis of the moving jet. A numerical method is used to compute fully nonlinear travelling solitary waves and comparisons with weakly nonlinear theories and experiments are presented. The time evolution of the axisymmetric nonlinear waves will be simulated.
47
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Session 2: Probl`emes `a fronti`ere libre
Obstacle type problems for minimal surfaces
SAVIN Ovidiu
Columbia University, USA
We describe certain obstacle type problems involving a standard and a nonlocal minimal surface. We discuss optimal regularity of the solution and a characterization of the free boundary.
Global bifurcation of gravity water waves with multiple critical layers
VARHOLM Kristoffer, BR ¨ ULL Gabriele
Norwegian University of Science and Technology, Norway
We establish the existence of global curves of steady periodic gravity water waves with an affine vorticity distribution, extending previous results for small-amplitude waves. The formulation used allow for waves with an arbitrary number of critical layers, at least sufficiently close to the bifurcation point. This is a work in progress.
The obstacle problem for the fractional Laplacian with drift
VEGA SMIT Mariana
University of Duisburg-Essen, Germany
We present the C1,α regularity of the regular part of the free boundary in the obstacle problem defined by the fractional Laplacian operator with gradient perturbation, in the subcritical regime (s∈(1/2,1)). More specifically, we consider
min{Lu, u−ϕ}= 0, where we denote Lu:= (−∆)su+hb(x),∇ui+c(x)u.
Our proof relies on a new Weiss-type monotonicity formula and an epiperimetric inequality. Both are generalizations of the ideas of G. Weiss, used in the classical obstacle problem for the Laplace operator, to our framework of fractional powers of the Laplace operator with drift.
48
XIII-`eme Colloque Franco-Roumain de Math´ematiques Appliqu´ees, Ia¸si 2016
Session 2: Probl`emes `a fronti`ere libre
Regularity of the optimal sets for spectral functionals
VELICHKOV Bozhidar
Universit´e Grenoble Alpes, France
We prove that the optimal set for the sum of Dirichlet eigenvaluesλ1+· · ·+λk, among all sets of prescribed Lebesgue measure, has a boundary which is C1,α regular up to a set of small dimension.
Properties of solitary waves in deep water
WHEELER Miles
Courant Institute of Mathematical Sciences, USA
We consider two- and three-dimensional solitary water waves in infinite depth, both with and without surface tension. Under an assumption that the free surface and velocity potential decay algebraically, we show that the velocity potential behaves like a dipole with a nonzero “dipole moment” related to the kinetic energy.
This implies that the angular momentum is infinite, and also gives related asymptotics for the free surface:
In two dimensions it is positive near infinity while in three dimensions it changes sign. These conclusions complement previous nonexistence results for three-dimensional solitary waves without surface tension.
49
Session 3
Mod` eles math´ ematiques et m´ ethodes num´ eriques en m´ ecanique des milieux continus
Organisateurs:
Mircea Sofonea (Perpignan) Cristian Faciu (Bucarest)
M´ ethode multigrille pour les in´ egalit´ es contenant un terme non-diff´ erentiable
BADEA Lori
Institut de Math´ematiques de l’Acad´emie Roumaine, Roumanie
Au d´ebut, nous introduisons et prouvons la convergence globale de certaines m´ethodes multiniveaux et multigrilles pour les in´egalit´es variationnelles (de la premi`ere esp´ece). Les m´ethodes sont introduites comme des algorithmes de correction sur les sousespaces dans un espace de Banach r´eflexif, o`u de r´esultats g´en´eraux de convergence sont d´eriv´es. Ces algorithmes deviennent des m´ethodes multigrille et multiniveaux en introduisant les espaces d’´el´ements finis. Dans ce cas, les taux globaux de convergence sont ´ecrits en fonction du nombre de niveaux.
Une extension directe de ces m´ethodes aux in´egalit´es variationnelles de la deuxi`eme esp´ece et aux in´egalit´es quasi-variationnelles n’est pas tr`es ´evidente, mais pour eux, nous pouvons introduire certaines m´ethodes multigrilles qui sont bas´ees sur celles pr´ec´edement d´ecrites. En utilisant des lin´earisations de Newton de la fonctionnelle non-diff´erentiable, R. Kornhuber a introduit des m´ethodes multigrilles pour les probl`emes de compl´ementarit´e et a estim´e leur taux de convergence asymptotique. Dans cet expos´e, nous estimons le taux de convergence globale d’une m´ethode multigrille pour le cas particulier des in´egalit´es quasi-variationnelle lorsque l’in´egalit´e contient un terme donn´e par un op´erateur de contraction. En outre, nous introduisons un algorithme multigrille pour les in´egalit´es variationnelles de la deuxi`eme esp´ece bas´e sur la r´egularisation de Moreau du terme non-diff´erentiable de l’in´egalit´e. De cette fa¸con, nous obtenons une in´egalit´e variationnelle de la premi`ere esp`ece. Nous montrons que la solution du probl`eme r´egularis´e converge vers la solution du probl`eme initial et pour le r´esoudre, nous consid´erons la m´ethode multigrille d´ej`a ´etudi´e.
Les exp´eriences num´eriques ont montr´e une tr`es bonne convergence de la m´ethode, mˆeme pour de valeurs du param`etre de r´egularisation proches de z´ero.
