Régis MONNEAU

Régis MONNEAU

Organization:

Research Unit:

Project:

EDP et matériaux

Phone:

Fax:

E-mail:

monneau_AT_cermics.enpc.fr

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Lectures of Luis A. Caffarelli: April 11-15, 2011

Research topics

Elasticity and dislocation dynamics
Nonlinear elliptic partial differential equations and free boundary problems (see the web site FBP news)

Organization/Participation to projects

Scientific coordinator of the team "EDP et matériaux" at CERMICS (see PDE and Materials group).
Member of the project ANR MICA "Mouvement d'interfaces, Calcul et Applications" (inter-laboratories)
Associate member to the project POLONIUM (2009-2010) (cooperation with Poland)
Previous projects

Diplomas and academic potitions

Engineer of Ecole Polytechnique (X90), Engineer of "Ponts et Chaussées" (1996), Civil-engineer in chief of "Ponts et Chaussées" (2006).
PhD thesis of Paris VI Universisty (1999): Free boundary problems, nonlinear elliptic PDEs and applications to combustion, superconductivity and elasticity, advisors: Henri Berestycki and Alexis Bonnet.
Post-Doc position (2000) at Massachusetts Institute of Technology, in collaboration with David Jerison.
Habilitation à diriger les recherches (Paris VI University, 2002); qualifications sections 25 and 26.

Past and present PhD students

Adrien Blanchet

Amin Ghorbel, Numerical analysis of dilsocation dynamics and applications to homogenization, defended on january 12, 2007.
Nicolas Forcadel, Contribution to partial differential equations describing the motion of fronts and applications to dislocation dynamics, defended on july 2, 2007.
Ahmad El Hajj, Theoretical and numerical analysis of the dynamics of dislocation densities, with co-advisor Marco Cannone, defended on december 7, 2007.
Hassan Ibrahim, Analysis of parabolic/Hamilton-Jacobi systems modelizing the dynamics of dislocation densities in a bounded domain, with co-advisor Mustapha Jazar, defended on june 30, 2008.
Danny El Kass, Micro-macro analysis of nanotubes and dislocations, with co-advisors Cyril Imbert, Mustapha Jazar, Nicolas Forcadel.
Arnaud Le Guilcher, Front propagation methods and applications, with co-advisor Antonin Chambolle.
Mohammad Al Haj, Analysis of elasto-visco-platic models including dislocation dynamics modeling, with co-advisors Raafat Talhouk and Hassan Ibrahim.
Guillaume Costeseque, Traffic modeling: from microscopic to macroscopic, with co-advisor Jean-Patrick Lebacque.
Łukasz Paszkowski, Analytic and numerical study of dislocation dynamics, with main advisor Piotr Biler.
Ghada Chmaycem, Analysis and simulation of a model for seawater intrusion, with co-advider Mustapha Jazar.

Past and present post-doc students

Elisabetta Carlini (2004)
Mohammed El Rhabi (2005-2006)
Simone Cacace (2009)
Erik Lindgren (2009-2010)
Avetik Arakelyan (2011-2012)

Publications

(with F. Hamel) Solutions d'équations semilinéaires dans R^N ayant des courbes de niveau de forme conique, Comptes-Rendus de l'Académie des Sciences de Paris, t. 327, Série I, p. 645-650, (1998).
(with A. Bonnet) Distribution of vortices in a type II superconductor as a free boundary problem: Existence and regularity via Nash-Moser theory , Interfaces and Free Boundaries, 2, 181-200 (2000).
(with A. Bonnet and S.J. Chapman) Convergence of Meissner minimisers of the Ginzburg-Landau energy as kappa tends to infinity, Comptes-Rendus de l'Académie des Sciences de Paris, t. 331, Série I, p. 1-5, (2000).
(with F. Hamel) Solutions of semilinear elliptic equations in R^N with conical-shaped level sets, Communications in Partial Differential Equations, 25 (5&6), 769-819 (2000).
(with A. Bonnet and S.J. Chapman) Convergence of Meissner minimisers of the Ginzburg-Landau energy of superconductivity as kappa tends to infinity, SIAM Journal of Mathematical Analysis, Vol. 31, No 6, 1374--1395 (2000).
(with H. Berestycki and F. Hamel) One-dimensional symmetry for some bounded entire solutions of some elliptic equations, Duke Mathematical Journal, 103 (3), 375-396 (2000).
(with J. Dolbeault)Estimations de convexité pour des équations elliptiques non-lineaires et application à des problèmes de frontière libre, Comptes-Rendus de l'Académie des Sciences de Paris, t. 331, Série I, p. 771-776, (2000).
(with D.S. Jerison) L'existence d'un minimiseur global symétrique sur R^{n-1} implique l'existence d'un contre-exemple à une conjecture de De Giorgi dans R^n, Comptes-Rendus de l'Académie des Sciences de Paris, t. 333, Série I, p. 427-431, (2001).
A Brief Overview on the Obstacle Problem, in Proceedings of the Third European Congress of Mathematics, Barcelona, (2000): Progress in Mathematics. Vol 202, Birkhäuser Verlag Basel/Switzerland, 303-312 (2001).
(with X. Blanc) Screening of an Applied Electric Field Inside a Metallic Layer Described by the Thomas-Fermi-von Weizsäcker Model, Advances in Differential Equations , Vol 7 (7), pp 847-876, (2002).
Estimations intérieures with régularité optimale pour un modèle de plaques en élasticité linéaire, Comptes-Rendus de l'Académie des Sciences de Paris, Ser. I 334 (2002) 1-6.
Justification de la théorie non linéaire de Kirchhoff-Love comme application d'une nouvelle méthode d'inversion singulière, Comptes-Rendus de l'Académie des Sciences de Paris, Ser. I 334 (2002) 615-620.
(with F. Hamel) Existence and uniqueness for a free boundary problem arising in combustion theory, Interfaces and Free Boundaries, 4, (2002), 167-210.
(with J. Dolbeault) Convexity Estimates for Nonlinear Elliptic Equations and Application to Free Boundary Problems, Ann. I.H. Poincaré, Analyse Non Linéaire, 19 (6), 903-926 (2002).
(with F. Hamel) Conical-shaped travelling fronts applied to the mathematical analysis of the shape of premixed Bunsen flames, In : Nonlinear PDE's in Physics, H. Berestycki and Y. Pomeau eds., NATO ASI Series, Elsevier Publ. Co., Doordrecht, 169-187, (2002).
Quasilinear Elliptic System Arising in a Three-dimensional Type-II Superconductor for Infinite Kappa, Nonlinear Analysis, T.M.A., Vol. 52, 3, 917-930, (2002).
(with F. Legoll) Designing reversible measure invariant algorithms with applications to molecular dynamics, Journal of Chemical Physics, Vol. 117 (23), 10452-10464, (2002).
(with A. Gaudiello, J. Mossino, F. Murat , A. Sili) On the junction of elastic plates and beams , Comptes-Rendus de l'Académie des Sciences de Paris, Ser. I 335 (2002) 717-722.
(with J. Dolbeault) On a Liouville type theorem for isotropic homogeneous fully nonlinear elliptic equations in dimension two , Annali della Scuola Normale Superior di Pisa, Classe di Scienze (5) Vol. II (2003), pp. 181-197.
On the Number of Singularities for the Obstacle Problem in Two Dimensions, Journal of Geometric Analysis, 13 (2), (2003), 359-389.
Justification of the nonlinear Kirchhoff-Love theory of plates as the application of a new singular inverse method, Archive for Rational Mechanics and Analysis 169 (2003) 1-34.
(with A. Bonnet) On the Mushy Region Arising Between Two Fluids in a Porous Medium , Nonlinear Analysis, Real World and Applications Vol. 5, Issue 1, (2004), 159-182.
On the Regularity of a Free Boundary for a Nonlinear Obstacle Problem Arising in Superconductor Modelling , Annales de la Faculté des Sciences de Toulouse, (6) 13 (2004), no. 2, 289-311.
(with D.S. Jerison) Towards a counter-example to a conjecture of De Giorgi in high dimensions , Annali di Matematica Pura ed Applicata 183, 439-467 (2004); published online, April 27, (2004).
(with O. Alvarez, P. Hoch, Y. Le Bouar) Existence et unicité en temps court d'une solution de viscosité discontinue d'une équation de Hamilton-Jacobi non locale décrivant la dynamique d'une dislocation., Note C.R. Acad. Sci. Paris, Ser. I 338 (2004) 679-684.
(with F. Hamel and J.-M. Roquejoffre) Stability of travelling waves in a model for conical flames in two space dimensions , Ann. Scient. Ec. Norm. Sup. 4ème série, t. 37, 469-506, (2004).
(with R. Benguria, I. Catto, J. Dolbeault) Oscillating minimizers of a fourth order problem invariant under scaling, J. Differential Equations 205 (2004) 253-269.
Uniform Elliptic Estimate for an Infinite Plate in Linear Elasticity, Communications in Partial Differential Equations 29 (7-8) 989-1016, (2004).
(with F. Hamel, J.-M. Roquejoffre) Existence et propriétes qualitatives de fronts coniques bistables en dimension 2 d'espace, Note C.R. Acad. Sci. Paris, Ser. I 339 (2004) 699-704.
(with J. Dolbeault, P. Felmer) Symmetry and non-uniformly elliptic operators, Differential and Integral equations, Volume 18, Number 2, 141-154 (2005).
(with H. Shahgholian) Non-convexity of level sets in convex rings for semilinear elliptic problems , Indiana Univ. Math. J. 54 (2), 465-471 (2005).
(with A. Ghorbel) Equation d'Hamilton-Jacobi non-locale modélisant la dynamique des dislocations, proceeding of the conference "Tendances des Applications Mathématiques en Tunisie, Algérie, Maroc" 2005, Ed. ENIT-LAMSIN, 322-328 (2005).
(with O.Alvarez, E.Carlini, P.Hoch, Y.Le Bouar) Dislocation dynamics described by non-local Hamilton-Jacobi equations, Materials Science & Engineering: A , Volumes 400-401, 25 July 2005, pages 162-165.
(with F. Hamel, J.-M. Roquejoffre) Existence and qualitative properties of multidimensional conical bistable fronts, Disc. Cont. Dynam. Systems 13 (2005), 1069-1096.
(with A. Blanchet, J. Dolbeault) On the one-dimensional parabolic obstacle problem with variable coefficients, Elliptic and Parabolic Problems A Special Tribute to the Work of Haim Brezis Series: Progress in Nonlinear Differential Equations and Their Applications, Vol. 63, pages 59-66, C. Bandle and al. (Eds.), Birkhäuser, (2005).
(with O.Alvarez, P. Cardaliaguet) Existence and uniqueness for dislocation dynamics with nonnegative velocity, Interfaces and Free Boundaries, 7 (4), 415-434, (2005).
(with A. Ghorbel, M. El Rhabi) Comportement mécanique par homogénéisation de la dynamique des disclocations, Proceeding of the national conference "MECAMAT" - Aussois 2006, Ecole de Mécanique des Matériaux - Aussois 2006 (janvier 2006, Aussois, France).
(with F. Hamel, J.-M. Roquejoffre) Asymptotic properties and classification of bistable fronts with Lipschitz level sets, Disc. Cont. Dynam. Systems 14 (2006), 75-92.
(with A. Blanchet and J. Dolbeault) On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients, Journal de Mathématiques Pures and Appliquées 85 (3), 371-414, (2006).
(The version on this web page is correct, but there is an erratum for the published version).
(with O.Alvarez, P.Hoch, Y.Le Bouar) Dislocation dynamics: short time existence and uniqueness of the solution, Archive for Rational Mechanics and Analysis 181 (3), (2006), 449-504.
(with O. Alvarez, E. Carlini, E. Rouy) Convergence of a first order scheme for a non local eikonal equation, IMACS Journal "Applied Numerical Mathematics" 56, 1136-1146, (2006).
(with P. Cardaliaguet, F. Da Lio, N. Forcadel) Dislocation dynamics : a non-local moving boundary, proceedings of the conference FBP 2005, Coimbra, Portugal, International Series of Numerical Mathematics, Vol. 154, Birkhäuser Verlag Basel/Switzerland, 125-135, (2006).
Some Remarks on the Asymptotic Inversibility of the Linearized Operator of Nonlinear Elasticity in the Context of the Displacement Approach, Z. Angew. Math. Mech. 86 (5), 400-409, 2006.
(with O. Alvarez, E. Carlini, E. Rouy) A convergent scheme for a non local Hamilton Jacobi equation modelling dislocation dynamics, Numerische Mathematik 104 (4), 413-444, 2006.
A new 3d-2d interior error estimate independent on the geometry of a linear elastic plate, Asymptotic Analysis 49 (3,4), (2006), 331-344.
(with A. El Soufi and M. Jazar) A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions, Annales de l'I.H.P., Analyse non linéaire 24 (1), 17-39, (2007).
(with A. Gaudiello, J. Mossino, F. Murat, A. Sili) Junction of elastic plates and beams , ESAIM: Control, Optimisation and Calculus of Variations, 13 (3), 419-457, (2007).
(with G.S. Weiss) An Unstable Elliptic Free Boundary Problem arising in Solid Combustion, Duke Mathematical Journal 136(2), 321-341, (2007).
(with G. S. Weiss) Self-propagating High temperature Synthesis (SHS) in the high activation energy regime, Proceedings of EQUADIFF 11, Acta Math. Univ. Comenianae, Vol. LXXVI, 1, 99-109, (2007).
A transport formulation for moving fronts and application to dislocations dynamics, Interfaces and Free Boundaries, 9, 383-409, (2007).
Méthodes géométriques pour les problèmes à frontières libres, (Summer school CIMPA 2004), Aspects théoriques et appliqués de quelques EDP issues de la géométrie ou de la physique, p. 119-156, Séminaires et congrès, collection SMF, Numéro 17, Ed. A. El Soufi et M. Jazar, SMF 2009.
(with C. Imbert) Homogenization of first order equations with u/epsilon-periodic Hamiltonians. Part I: local equations, Archive for Rational Mechanics and Analysis, 187 (1), 49-89, (2008).
(with G. Barles, P. Cardaliaguet, O. Ley) General existence results and uniqueness for dislocation equations, SIAM J. Math. Anal. 40 (1), 44-69, (2008).
(with F. Da Lio, N. Forcadel) Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics, Journal of the European Mathematical Society 10 (4), (2008), 1061-1104.
(with C. Imbert, E. Rouy) Homogenization of first order equations with u/epsilon-periodic Hamiltonians. Part II: application to dislocations dynamics., Communications in Partial Differential Equations 33 (2008), no. 1-3, 479-516.
(with A. Ghorbel, P. Hoch) A numerical study for the homogeneization of one-dimensional models describing the motion of dislocations, Int. J. of Computing Science and Mathematics 2 (1-2) (2008), 28-52.
(with E. Carlini, M. Falcone, N. Forcadel) Convergence of a Generalized Fast Marching Method for an Eikonal equation with a Velocity Changing Sign, SIAM J. Numer. Anal. 46 (6), (2008), 2920-2952.
Nouvelle méthode numérique pour le calcul de la dynamique des dislocations, dossier de recherche de l'Ecole des ponts, no. 18, (2008).
(with G. S. Weiss) Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion, Ann. I.H. Poincaré, Analyse Non Linéaire 26 (4) (2009), 1207-1222.
(with N. Forcadel, C. Imbert) Homogenization of the dislocation dynamics and of some particle systems with two-body interactions, Discrete and Continuous Dynamical Systems - A, vol. 23 (3) (March 2009), 785 - 826.
(with A. El Hajj and H. Ibrahim) Derivation and study of dynamical models of dislocation densities, (proceedings of CANUM 2008), ESAIM: Proceedings, Vol. 27 (May 2009), p. 227-239.
(with N. Forcadel and C. Imbert) Homogenization of fully overdamped Frenkel-Kontorova models, Journal of Differential Equations 246 (3) (1 February 2009), 1057-1097.
(with H. Ibrahim and M. Jazar) Global existence of solutions to a singular parabolic/Hamilton-Jacobi coupled system with Dirichlet conditions, C. R. Acad. Sci. Paris, Ser. I 346 (2008) 945-950.
(with N. Forcadel) Existence of solutions for a model describing the dynamics of junctions between dislocations, SIAM J. Math. Anal. 40 (2009), no. 6, 2517-2535.
(with R. Benguria and J. Dolbeault) Harnack inequalities and discrete-continuum error estimates for a chain of atoms with two-body interactions, J. Statistical Physics 134 (1) (2009), 27-51.
(with N. Forcadel, C. Imbert) Viscosity solutions for particle systems and homogenization of dislocation dynamics, accepted contribution to the collective book "On the notions of solutions to nonlinear elliptic problems: results and developments", Quaderni di Matematica 23, publication of the Department of Mathematics of the Seconda Universita di Napoli, Caserta (2008). Editors: A. Alvino, A. Mercaldo, F. Murat, I. Peral.
(with H. Ibrahim) On a parabolic logarithmic Sobolev inequality, Journal of Functional Analysis 257 (3) (2009), 903-930.
(with A. Briani) Time-homogenization of a first order system arising in the modelling of the dynamics of dislocation densities, C. R. Acad. Sci. Paris, Ser. I 347 (2009) 231-236.
Pointwise estimates for Laplace equation. Applications to the free boundary of the obstacle problem with Dini coefficients , Journal of Fourier Analysis and Applications 15 (3) (2009), 279-335.
(with N. Forcadel, C. Imbert) Recent results on dislocations dynamics and homogenization, proceedings of ICIAM 2007 (see web site), (2009).
(with M. Cannone, A. El Hajj, F. Ribaud) Global existence for a system of non-linear and non-local transport equations describing the dynamics of dislocation densities , Arch. Rational Mech. Anal. 196 (2010), 71-96.
(with P. Biler and G. Karch) Nonlinear diffusion of dislocation density and self-similar solutions, Communications in Mathematical Physics 294 (1) (2010),145-168.
(with A. El Hajj and H. Ibrahim) Homogenization of dislocation dynamics, proceedings of the conference Dislocations 2008 (Hong Kong), IOP Conferences Series: Materials Science and Engineering, 3 (2009) 012023.
(with A. El Hajj and H. Ibrahim) Dislocation dynamics: from microscopic models to macroscopic crystal plasticity, Continuum Mechanics and Thermodynamics 21 (2) (2009), 109-123.
(with A. Ghorbel) Well-posedness and numerical analysis of a one-dimensional non-local transport equation modelling dislocations dynamics, Mathematics of Computation vol. 79, no. 271, (2010), 1535-1564.
(with H. Ibrahim and M. Jazar) Dynamics of dislocation densities in a bounded channel. Part II: existence of weak solutions to a singular parabolic/Hamilton-Jacobi strongly coupled system, Comm. Partial Differential Equations 34 (8) (2009), 889-917.
(with H. Ibrahim and M. Jazar) Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system, Comm. Pure Appl. Anal. 9 (3) (May 2010), 703-719.
(with A. El Hajj) Global continuous solutions for diagonal hyperbolic systems with large and monotone data, Journal of Hyperbolic Differential Equations 7 (1) (2010), 1-26.
(with H. Ibrahim) On the rate of convergence in periodic homogenization of scalar first-order ordinary differential equations, SIAM J. Math. Anal. 42 (5) (2010), 2155-2176.
(with N. Forcadel, C. Imbert) Homogenization of accelerated Frenkel-Kontorova models with n types of particles, accepted to Transactions of the AMS.
(with N. Alibaud, A. Briani) Diffusion as a singular homogenization of the Frenkel-Kontorova model, J. Differential Equations 251 (2011), 785-815.
Introduction to the Fast Marching Method, accepted for publication in the procedings of the summer school CIMPA 2010, Tripoli, Lebanon.
(with A. Chambolle, E. Lindgren) The Holder infinite Laplacian and Holder extensions, accepted for publication in ESAIM-COCV.
(with E. Carlini, N. Forcadel) A Generalized Fast Marching Method for dislocation dynamics, SIAM J. Numer. Anal. 49 (6) (2011), 2470-2500.
(with M.d.M. Gonzalez) Slow motion of particle systems as a limit of a reaction-diffusion equation with half-Laplacian in dimension one, DCDS-A 32 (4) (2012), 1255-1286.
(with A. Fino, H. Ibrahim) The Peierls-Nabarro model as a limit of a Frenkel-Kontorova model, accepted to JDE.
(with S. Cacace, A. Chambolle) A posteriori error estimates for the effective Hamiltonian of dislocation dynamics, accepted to Numerische Mathematik.
(with C. Imbert, H. Zidani) A Hamilton-Jacobi approach to junction problems and application to traffic flows, accepted to ESAIM-COCV.

Preprints

(with F. Murat and A. Sili) Error estimates for the 3d-1d dimension reduction in anisotropic heterogeneous linearized elasticity, (preliminary version, 2002).
(with N. Forcadel, C. Imbert) Uniqueness and existence of spirals moving by forced mean curvature motion, submitted to Interfaces and Free Boundaries.
(with S. Patrizi) Homogenization of the Peierls-Nabarro model for dislocation dynamics, submitted to J. Differential Equations.
(with S. Patrizi) Derivation of Orowan's law from the Peierls-Nabarro model, submitted to CPDE.
(with A. El Hajj) Some uniqueness results for diagonal hyperbolic systems with large and monotone data, submitted to JMPA.
(with M. Jazar) Formal derivation of seawater intrusion models, preprint HAL.
(with J.-M. Roquejoffre, V. Roussier-Michon) Travelling graphs for the forced mean curvature motion in an arbitrary space dimension, submitted to Annales Scientifiques de l'Ecole Normale Supérieure.
(with E. Lindgren) Pointwise estimates for the heat equation. Application to the free boundary of the obstacle problem with Dini coefficients, submitted to Indiana Univ. Math. J.

CERMICS ENPC
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77455 MARNE LA VALLEE Cedex 2
Tel : +33 (0)1-64-15-35-80 Fax : +33 (0)1-64-15-35-86

monneau_AT_cermics.enpc.fr