PLEASE DO NOT USE MY EMAIL TO CONTACT ME. YOU CAN USE MY MAIL ADDRESS.
Régis MONNEAU
- Project: PDEs and materials
- Mail:
24, rue E. Béliard,
91150 Etampes
(FRANCE)
Some research topics
- PDEs on networks, application to traffic
- Elasticity and dislocation dynamics
- Nonlinear elliptic partial differential equations and free boundary problems
Organization/Participation to projects
Diplomas and academic potitions
Past and present PhD students
- Adrien Blanchet,
Monotonicity formulas applied to free boundary problems and to modelling in biology,
with co-advisor Jean Dolbeault;
defended on December 12, 2005.
- 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,
Atomic to continuum passage for nanotubes. A discrete Saint-Venant principle and error estimates,
with co-advisor
Mustapha Jazar, defended on December 10, 2012.
- Arnaud Le Guilcher,
Front propagation methods and applications,
with co-advisor
Antonin Chambolle, defended on June 16, 2014.
- Mohammad Al Haj,
Analysis of elasto-visco-platic models including dislocation dynamics modeling,
with co-advisors Raafat Talhouk and Hassan Ibrahim, defended on June 17, 2014.
- Guillaume Costeseque,
Traffic modeling: from microscopic to macroscopic,
with co-advisor Jean-Patrick Lebacque, defended on September 12, 2014.
- Łukasz Paszkowski,
Analytic and numerical study of dislocation dynamics,
co-advisor with Piotr Biler as main advisor, exam on June 2, 2014, defended on September 16, 2014.
- Ghada Chmaycem,
Study of the porous medium equation and of a blister model,
with co-advisor Mustapha Jazar, defended on September 18, 2014.
- Eleftherios Ntovoris,
Erosion and growth of crystals, co-advisor with M. Cannone as main advisor, defended on September 12, 2016.
- Jana Alkhayal,
Seawater intrusion models, co-advisor with M. Jazar, and with D. Hilhorst as main advisor, defended on November 24, 2016.
- Jeremy Firozaly,
Homogenization of vehicular models and green waves,
co-advisor with C. Imbert as main advisor, defended on December 15, 2017.
- Ali Assi,
Homogenization of traffic and Green waves co-advisor with N. Forcadel as main advisor,
started in September 2024.
Past and present post-doc students
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).
The result is only valid in dimension N=2 (see Erratum).
- (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, (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. Alibaud, A. Briani)
Diffusion as a singular homogenization of the
Frenkel-Kontorova model,
J. Differential Equations 251 (2011), 785-815.
- (with E. Carlini, N. Forcadel)
A Generalized Fast Marching Method for dislocation dynamics,
SIAM J. Numer. Anal. 49 (6) (2011), 2470-2500.
-
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, ESAIM-COCV 18 (3) (2012), 799-835.
- (with N. Forcadel, C. Imbert)
Homogenization of accelerated Frenkel-Kontorova models
with n types of particles,
Transactions of the AMS 364 (12) (2012), 6187-6227.
- (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,
JDE 252 (1) (2012), 258-293.
- (with S. Cacace, A. Chambolle)
A posteriori error estimates for the effective
Hamiltonian of dislocation dynamics, Numerische Mathematik 121 (2) (2012), 281-335.
- (with C. Imbert, H. Zidani)
A Hamilton-Jacobi approach to junction problems and application to traffic flows, ESAIM-COCV 19 (2013), 129-166.
- (with S. Patrizi)
Derivation of Orowan's law from the Peierls-Nabarro model, CPDE 37 (10) (2012), 1887-1911.
- (with N. Forcadel, C. Imbert)
Uniqueness and existence of spirals moving by forced mean curvature motion,
Interfaces and Free Boundaries 14 (2012), 365-400.
- (with E. Lindgren)
Pointwise estimates for the heat equation.
Application to the free boundary of the obstacle problem
with Dini coefficients, Indiana Univ. Math. J. 62 (1) (2013), 1-29.
- (with S. Patrizi)
Homogenization of the Peierls-Nabarro model for dislocation dynamics,
J. Differential Equations 253 (7) (2012), 2064-2105.
- (with J.-M. Roquejoffre, V. Roussier-Michon)
Travelling graphs for the forced mean
curvature motion in an arbitrary space dimension,
Ann. Scient. Ec. Norm. Sup. 4e serie, t. 46, (2013), 215-246.
- (with S. Issa, M. Jazar)
Existence of supersonic traveling waves for the Frenkel-Kontorova model,
Differential and Integral Equations 26 (3-4) (2013), 321-353.
- (with M. Al Haj, N. Forcadel)
Existence and uniqueness of traveling waves for fully overdamped Frenkel-Kontorova models,
Archive for Rational Mechanics and Analysis 210 (1) (2013), 45-99.
- (with A. El Hajj)
Some uniqueness results for diagonal hyperbolic systems with
large and monotone data, JHDE 10 (3) (2013), 461-494.
-
Forced mean curvature motions: 1. Homogenization, 2. Spirals,
Oberwolfach reports No. 15/2013, Meeting "Interfaces and free boundaries; analysis, control and simulation", (2013).
- (with M. Al Haj, N. Forcadel, C. Imbert)
Modele de Frenkel-Kontorova : resultats d'homogeneisation et existence de traveling waves, Equations aux derives partielles et leurs applications, Actes du colloque Edp-Normandie. Le Havre 2012. 51-60. FNM Federation Normandie Mathematiques (2013).
- (with M. Roussignol, A. Tordeux)
Invariance and homogenization of an adaptive time gap car-following model, NoDEA 21 (4) (2014), 491-517.
- (with L.A. Caffarelli)
Counter-example in three dimension and homogenization of geometric motions in two dimension, (long version);
short version in: ARMA 212 (2) (2014), 503-574.
- (with D. El Kass)
Atomic to continuum passage for nanotubes. A discrete Saint-Venant principle and error estimates,
ARMA 213 (1) (2014), 25-128.
- (with M. Jazar)
Derivation of seawater intrusion models by formal asymptotics, SIAM J. Appl. Math. 74 (4) (2014), 1152-1173.
- (with H. Ibrahim)
Reduced ODE dynamics as formal relativistic asymptotics of a Peierls-Nabarro model,
European Journal of Applied Mathematics 25 (4) (2014), 511-529.
- (with H. Berestycki, J.A. Scheinkman)
A non local free boundary problem
arising in a theory of financial bubbles (long version),
Phil. Trans. Royal Soc. A. 372 (2028) (2014).
- (with L. Monasse)
Gradient entropy estimate and convergence of a semi-explicit scheme for diagonal hyperbolic systems,
SIAM J. Numer. Anal. 52 (6) (2014), 2792-2814.
- (with A. Ghorbel)
Existence and non-existence of semi-discrete shocks for a car-following model in traffic flow,
SIAM J. Math. Anal. 46 (6) (2014), 3612-3639.
- (with G. Costeseque, J.-P. Lebacque)
A convergent scheme for Hamilton-Jacobi equations on a junction: application to traffic, Numer. Math. 129 (3) (2015), 405-447.
-
The method of differential contractions, CRAS. 353 (2) (2015), 143-147.
- (with E. Lindgren)
Pointwise regularity of the free boundary for the parabolic obstacle problem,
Calc. Var. 54 (1) (2015), 299-347.
- (with Y. Noumir, A. Le Guilcher, N. Lardjane, A. Sarrazin)
(preprint version)
A fast-marching like algorithm for Geometrical Shock Dynamics,
J. Computational Physics 284 (2015), 206-229.
- (with H. Hajj Chehade, M. Jazar)
A priori gradient bounds for fully nonlinear parabolic equations and applications to porous medium models,
JMPA 103 (6) (2015), 1346-1357.
- (with N. Forcadel, C. Imbert)
Steady state and long time convergence of spirals moving by forced mean curvature motion,
CPDE 40 (6) (2015), 1137-1181.
- (with G. Galise, C. Imbert)
A junction condition by specified homogenization,
Analysis and PDE 8 (8) (2015), 1891-1929.
- (with G. Chmaycem, M. Jazar)
A new contraction family for porous medium and fast diffusion equation,
ARMA 221 (2) (2016), 805-815.
- (with G. Chmaycem, M. Jazar)
Explicit phase diagram for a one-dimensional blister model, ZAMM 97 (2) (2017), 202-216.
- (with C. Imbert)
Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks, Annales scientifiques de l'ENS 50 (2) (2017), 357-448.
- (with C. Imbert)
Quasi-convex Hamilton-Jacobi equations posed on junctions: the
multi-dimensional case, DCDS-A, 37 (2017), 6405-6435.
- (with J. Alkhayal, S. Issa, M. Jazar)
Existence result for degenerate cross-diffusion system with application to seawater intrusion, ESAIM Control
Optim. Calc. Var. 24 (2018), no. 4, 1735-1758.
- (with H. Berestycki, C. Bruggeman, J.A. Scheinkman)
Bubbles in assets with finite life, Mathematics and
Financial Economics, 13 (2019), 429-558. (co-authors are warmly thanked)
- (with E. Ntovoris)
A solution with free boundary for non-Newtonian fluids with
Drucker-Prager plasticity criterion, ESAIM: COCV 25 (2019) 46, 37 pages.
- 2014-2022: how severe degradation of your working conditions
can affect your health?
- (with M. Al Haj)
The velocity diagram for traveling waves, (CRM)
Comptes Rendus. Mathématique, Tome 361 (2023), 777-782.
- (with M. Al Haj)
Velocity diagram of traveling waves for discrete reaction-diffusion
equations, (NoDEA), Nonlinear Differ. Equ. Appl. 30, 73
(2023), https://doi.org/10.1007/s00030-023-00871-x.
- (with M. Al Haj)
Traveling waves for discrete reaction-diffusion equations in the
general monostable case, J. Differ. Equ. 378 (2024),
707-756.
- (with N. Forcadel and C. Imbert)
Coercive Hamilton-Jacobi equations in domains: the twin blow-ups
method, C.R. Math. 362 (2024), 829-839.
- (with P. Cardaliaguet, N. Forcadel and T. Girard)
Conservation law and Hamilton-Jacobi equations on a junction: the
convex case, DCDS 44 (12) (2024), 3920-3961.
- (with P. Cardaliaguet, N. Forcadel)
A class of germs arising from homogenization in traffic flow on
junctions, JHDE 21 (02) (2024), 189-254.
- (with N. Forcadel and C. Imbert)
Non-convex coercive Hamilton-Jacobi equations: Guerand's relaxation
revisited, Pure and Applied Analysis 6 (4) (2024), 1055-1089.
- (with N. Forcadel and C. Imbert)
The twin blow-up method for Hamilton-Jacobi equations in higher
dimension, ESAIM:COCV 31 (2025) 12, *-*.
- (with N. Forcadel)
Beyond uniqueness: Relaxation calculus of junction conditions for
coercive Hamilton-Jacobi equations, JDE 456 (2026), 113964, 1-43.
Preprints