PLEASE DO NOT USE MY EMAIL TO CONTACT ME. YOU CAN USE MY MAIL ADDRESS.
Régis MONNEAU
Régis MONNEAU
Research topics
 PDEs on networks
 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 HJnet
"HamiltonJacobi equations on heterogeneous structures and networks" (interlaboratories)
 Member of the project ANR Weak KAM "beyond HamiltonJacobi" (interlaboratories)
 Member of the project ANR Landquake "Modelling of Landslides and
generated earthquakes for detection and understanding of gravitational instabilities" (interlaboratories)
 Member of the project CEDRE 11EF45 L20:
"Study of saltwater/freshwater front propagation in lebanese coastal aquifers"
 Previous 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 coadvisor 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 coadvisor Marco
Cannone, defended on December 7, 2007.
 Hassan
Ibrahim, Analysis of parabolic/HamiltonJacobi systems modelizing the dynamics
of dislocation densities in a bounded domain,
with coadvisor Mustapha Jazar, defended on June 30, 2008.
 Danny El Kass,
Atomic to continuum passage for nanotubes. A discrete SaintVenant principle and error estimates,
with coadvisor
Mustapha Jazar, defended on December 10, 2012.
 Arnaud Le Guilcher,
Front propagation methods and applications,
with coadvisor
Antonin Chambolle, defended on June 16, 2014.
 Mohammad Al Haj,
Analysis of elastoviscoplatic models including dislocation dynamics modeling,
with coadvisors Raafat Talhouk and Hassan Ibrahim, defended on June 17, 2014.
 Guillaume Costeseque,
Traffic modeling: from microscopic to macroscopic,
with coadvisor JeanPatrick Lebacque, defended on September 12, 2014.
 Łukasz Paszkowski,
Analytic and numerical study of dislocation dynamics,
coadvisor 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 coadvisor Mustapha Jazar, defended on September 18, 2014.
 Eleftherios Ntovoris, Erosion and growth of crystals, coadvisor with M. Cannone as main advisor, defended on September 12, 2016.
 Jana Alkhayal, Seawater intrusion models, coadvisor with M. Jazar, and with D. Hilhorst as main advisor, defened on November 24, 2016.
 Jeremy Firozaly, Homogenization of vehicular models and green waves, coadvisor with C. Imbert as main advisor.
Past and present postdoc students
Publications
 (with F. Hamel)
Solutions d'équations semilinéaires dans R^N ayant des courbes de
niveau de forme conique,
ComptesRendus de
l'Académie des Sciences de Paris, t. 327, Série I, p. 645650, (1998).
 (with A. Bonnet) Distribution of vortices in a type II
superconductor as a free boundary problem:
Existence and regularity via NashMoser theory , Interfaces and
Free Boundaries, 2, 181200 (2000).
 (with A. Bonnet and S.J. Chapman) Convergence of
Meissner minimisers of the GinzburgLandau energy as kappa tends to
infinity, ComptesRendus
de l'Académie des Sciences de Paris, t. 331, Série I, p. 15, (2000).
 (with F. Hamel) Solutions of
semilinear elliptic equations in R^N with conicalshaped level sets,
Communications in Partial
Differential Equations, 25 (5&6), 769819 (2000).
 (with A. Bonnet and S.J. Chapman) Convergence of
Meissner minimisers of the GinzburgLandau energy of superconductivity as
kappa tends to infinity, SIAM Journal of
Mathematical Analysis, Vol. 31, No 6, 13741395 (2000).
 (with H. Berestycki and F. Hamel) Onedimensional
symmetry for some bounded entire solutions of some elliptic
equations, Duke Mathematical
Journal, 103 (3), 375396 (2000).
 (with J. Dolbeault)Estimations de convexité pour
des équations elliptiques nonlineaires et application à des problèmes de
frontière libre, ComptesRendus
de l'Académie des Sciences de Paris, t. 331, Série I, p. 771776, (2000).
 (with D.S. Jerison) L'existence
d'un minimiseur global symétrique sur R^{n1} implique l'existence
d'un contreexemple à une conjecture de De Giorgi dans R^n,
ComptesRendus
de l'Académie des Sciences de Paris, t. 333, Série I, p. 427431,
(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, 303312 (2001).
 (with X. Blanc) Screening of an Applied Electric Field Inside a Metallic Layer
Described by the ThomasFermivon Weizsäcker Model, Advances in Differential
Equations , Vol 7 (7), pp 847876, (2002).
 Estimations
intérieures with régularité optimale pour un modèle de plaques en
élasticité linéaire,
ComptesRendus de l'Académie des Sciences de Paris, Ser. I 334 (2002) 16.
 Justification de la théorie non linéaire de
KirchhoffLove comme application d'une nouvelle méthode d'inversion
singulière,
ComptesRendus de l'Académie des Sciences de Paris, Ser. I 334 (2002) 615620.
 (with F. Hamel) Existence and uniqueness for a free boundary problem arising in
combustion theory, Interfaces and
Free Boundaries, 4, (2002), 167210.
 (with J. Dolbeault) Convexity
Estimates for Nonlinear Elliptic Equations and Application to Free
Boundary Problems, Ann. I.H. Poincaré,
Analyse Non Linéaire, 19 (6), 903926 (2002).
 (with F. Hamel) Conicalshaped
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, 169187, (2002).
 Quasilinear
Elliptic System Arising in a Threedimensional TypeII Superconductor
for Infinite Kappa, Nonlinear Analysis, T.M.A.,
Vol. 52, 3, 917930, (2002).
 (with F. Legoll) Designing reversible measure invariant algorithms with
applications to molecular dynamics, Journal of Chemical
Physics, Vol. 117 (23), 1045210464, (2002).
 (with A. Gaudiello, J.
Mossino, F. Murat , A. Sili) On the
junction of elastic plates and beams , ComptesRendus de
l'Académie des Sciences de Paris, Ser. I 335 (2002) 717722.
 (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. 181197.
 On the Number of Singularities
for the Obstacle Problem in Two Dimensions,
Journal of Geometric Analysis, 13
(2), (2003), 359389.
 Justification of the nonlinear KirchhoffLove theory of plates as the
application of a new singular inverse method, Archive
for Rational Mechanics and Analysis 169 (2003) 134.
 (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), 159182.
 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, 289311.
 (with D.S. Jerison) Towards a counterexample
to a conjecture of De Giorgi in high dimensions , Annali di
Matematica Pura ed Applicata 183, 439467 (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 HamiltonJacobi non locale décrivant la dynamique d'une
dislocation., Note C.R. Acad. Sci. Paris, Ser. I 338 (2004)
679684.
 (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, 469506, (2004).
 (with R. Benguria, I. Catto, J. Dolbeault) Oscillating
minimizers of a fourth order problem invariant under scaling, J. Differential Equations 205 (2004) 253269.
 Uniform Elliptic Estimate for an Infinite Plate in Linear
Elasticity, Communications in Partial
Differential Equations 29 (78) 9891016, (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) 699704.
 (with J. Dolbeault, P. Felmer) Symmetry and nonuniformly
elliptic operators, Differential and Integral equations, Volume 18,
Number 2, 141154 (2005).
 (with H. Shahgholian) Nonconvexity of level sets in
convex rings for semilinear elliptic problems
, Indiana Univ. Math. J. 54 (2), 465471 (2005).
 (with A.
Ghorbel) Equation d'HamiltonJacobi nonlocale modélisant la
dynamique des dislocations, proceeding of the conference
"Tendances des Applications Mathématiques en Tunisie, Algérie, Maroc"
2005, Ed. ENITLAMSIN, 322328 (2005).
 (with O.Alvarez, E.Carlini, P.Hoch, Y.Le Bouar) Dislocation
dynamics described by nonlocal HamiltonJacobi equations, Materials Science & Engineering: A , Volumes 400401, 25 July 2005, pages
162165.
 (with F. Hamel, J.M. Roquejoffre)
Existence
and qualitative properties of multidimensional conical bistable
fronts, Disc.
Cont. Dynam. Systems 13 (2005), 10691096.
 (with A. Blanchet, J. Dolbeault) On the onedimensional
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 5966, 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), 415434, (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), 7592.
 (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), 371414, (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), 449504.
 (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, 11361146, (2006).
 (with P. Cardaliaguet, F. Da Lio, N. Forcadel) Dislocation dynamics : a
nonlocal moving boundary,
proceedings of the conference FBP 2005, Coimbra, Portugal, International Series of
Numerical Mathematics, Vol. 154, Birkhäuser Verlag Basel/Switzerland, 125135, (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), 400409, 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), 413444, 2006.
 A new 3d2d
interior error estimate independent on the geometry of a linear elastic
plate, Asymptotic Analysis 49 (3,4), (2006), 331344.
 (with A. El Soufi and M. Jazar)
A Gammaconvergence argument for the blowup
of a nonlocal semilinear parabolic equation with Neumann boundary
conditions, Annales de l'I.H.P., Analyse non linéaire 24 (1), 1739, (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), 419457, (2007).
 (with G.S. Weiss) An
Unstable Elliptic Free Boundary Problem arising in Solid
Combustion, Duke Mathematical Journal 136(2), 321341, (2007).
 (with G. S. Weiss) Selfpropagating High temperature Synthesis (SHS) in the
high activation energy regime,
Proceedings of EQUADIFF 11, Acta Math.
Univ. Comenianae, Vol. LXXVI, 1, 99109, (2007).

A transport formulation for moving fronts
and application to dislocations dynamics,
Interfaces and
Free Boundaries, 9, 383409, (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. 119156,
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/epsilonperiodic Hamiltonians. Part I: local equations,
Archive for Rational Mechanics and Analysis, 187 (1), 4989, (2008).
 (with G. Barles, P. Cardaliaguet, O. Ley)
General existence results and uniqueness for dislocation equations,
SIAM J. Math. Anal. 40 (1), 4469, (2008).
 (with F. Da Lio, N. Forcadel)
Convergence of a nonlocal eikonal
equation to anisotropic mean curvature motion. Application to
dislocations dynamics,
Journal of the
European Mathematical Society 10 (4), (2008), 10611104.
 (with C. Imbert, E. Rouy)
Homogenization of first order equations
with u/epsilonperiodic Hamiltonians. Part II: application to dislocations
dynamics., Communications in Partial Differential Equations 33 (2008), no. 13, 479516.
 (with A. Ghorbel, P. Hoch)
A numerical study for the homogeneization of onedimensional models
describing the motion of dislocations, Int. J. of Computing Science and Mathematics
2 (12) (2008), 2852.
 (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), 29202952.
 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 reactiondiffusion system in solid combustion, Ann. I.H. Poincaré,
Analyse Non Linéaire 26 (4) (2009), 12071222.
 (with N. Forcadel, C. Imbert)
Homogenization of the dislocation
dynamics and of some particle systems with twobody 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. 227239.
 (with N. Forcadel and C. Imbert)
Homogenization of fully overdamped FrenkelKontorova models,
Journal of Differential Equations 246 (3) (1 February 2009), 10571097.
 (with H. Ibrahim and M. Jazar)
Global existence of solutions
to a singular parabolic/HamiltonJacobi coupled system with Dirichlet
conditions, C. R. Acad. Sci. Paris, Ser. I 346 (2008) 945950.
 (with N. Forcadel)
Existence of solutions for a model describing the dynamics of junctions between dislocations,
SIAM J. Math. Anal. 40 (2009), no. 6, 25172535.
 (with R. Benguria and J. Dolbeault)
Harnack inequalities and discretecontinuum error estimates for a chain of
atoms with twobody interactions,
J. Statistical Physics 134 (1) (2009), 2751.
 (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), 903930.
 (with A. Briani)
Timehomogenization of a first order system arising in the
modelling of the dynamics of dislocation densities,
C. R. Acad. Sci. Paris, Ser. I 347 (2009) 231236.

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), 279335.
 (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 nonlinear and nonlocal
transport equations describing the dynamics of dislocation densities
, Arch. Rational Mech. Anal. 196 (2010), 7196.
 (with P. Biler and G. Karch)
Nonlinear diffusion of dislocation density and selfsimilar solutions,
Communications in Mathematical Physics 294 (1) (2010),145168.
 (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), 109123.
 (with A. Ghorbel)
Wellposedness and numerical analysis of a onedimensional nonlocal transport equation modelling dislocations dynamics, Mathematics of Computation vol. 79, no. 271, (2010), 15351564.
 (with H. Ibrahim and M. Jazar)
Dynamics of dislocation
densities in a bounded channel. Part II: existence of weak solutions
to a singular parabolic/HamiltonJacobi strongly coupled system,
Comm. Partial Differential Equations 34 (8) (2009), 889917.
 (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), 703719.
 (with A. El Hajj)
Global continuous solutions for diagonal hyperbolic systems
with large and monotone data,
Journal of Hyperbolic Differential Equations 7 (1) (2010), 126.
 (with H. Ibrahim)
On the rate of convergence in periodic homogenization of
scalar firstorder ordinary differential equations,
SIAM J. Math. Anal. 42 (5) (2010), 21552176.
 (with N. Alibaud, A. Briani)
Diffusion as a singular homogenization of the
FrenkelKontorova model,
J. Differential Equations 251 (2011), 785815.
 (with E. Carlini, N. Forcadel)
A Generalized Fast Marching Method for dislocation dynamics,
SIAM J. Numer. Anal. 49 (6) (2011), 24702500.

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, ESAIMCOCV 18 (3) (2012), 799835.
 (with N. Forcadel, C. Imbert)
Homogenization of accelerated FrenkelKontorova models
with n types of particles,
Transactions of the AMS 364 (12) (2012), 61876227.
 (with M.d.M. Gonzalez)
Slow motion of particle systems as a limit of a reactiondiffusion
equation with halfLaplacian in dimension one,
DCDSA 32 (4) (2012), 12551286.
 (with A. Fino, H. Ibrahim)
The PeierlsNabarro model as a limit of a FrenkelKontorova model,
JDE 252 (1) (2012), 258293.
 (with S. Cacace, A. Chambolle)
A posteriori error estimates for the effective
Hamiltonian of dislocation dynamics, Numerische Mathematik 121 (2) (2012), 281335.
 (with C. Imbert, H. Zidani)
A HamiltonJacobi approach to junction problems and application to traffic flows, ESAIMCOCV 19 (2013), 129166.
 (with S. Patrizi)
Derivation of Orowan's law from the PeierlsNabarro model, CPDE 37 (10) (2012), 18871911.
 (with N. Forcadel, C. Imbert)
Uniqueness and existence of spirals moving by forced mean curvature motion,
Interfaces and Free Boundaries 14 (2012), 365400.
 (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), 129.
 (with S. Patrizi)
Homogenization of the PeierlsNabarro model for dislocation dynamics,
J. Differential Equations 253 (7) (2012), 20642105.
 (with J.M. Roquejoffre, V. RoussierMichon)
Travelling graphs for the forced mean
curvature motion in an arbitrary space dimension,
Ann. Scient. Ec. Norm. Sup. 4e serie, t. 46, (2013), 215246.
 (with S. Issa, M. Jazar)
Existence of supersonic traveling waves for the FrenkelKontorova model,
Differential and Integral Equations 26 (34) (2013), 321353.
 (with M. Al Haj, N. Forcadel)
Existence and uniqueness of traveling waves for fully overdamped FrenkelKontorova models,
Archive for Rational Mechanics and Analysis 210 (1) (2013), 4599.
 (with A. El Hajj)
Some uniqueness results for diagonal hyperbolic systems with
large and monotone data, JHDE 10 (3) (2013), 461494.

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 FrenkelKontorova : resultats d'homogeneisation et existence de traveling waves, Equations aux derives partielles et leurs applications, Actes du colloque EdpNormandie. Le Havre 2012. 5160. FNM Federation Normandie Mathematiques (2013).
 (with M. Roussignol, A. Tordeux)
Invariance and homogenization of an adaptive time gap carfollowing model, NoDEA 21 (4) (2014), 491517.
 (with L.A. Caffarelli)
Counterexample in three dimension and homogenization of geometric motions in two dimension, (long version);
short version in: ARMA 212 (2) (2014), 503574.
 (with D. El Kass)
Atomic to continuum passage for nanotubes. A discrete SaintVenant principle and error estimates,
ARMA 213 (1) (2014), 25128.
 (with M. Jazar)
Derivation of seawater intrusion models by formal asymptotics, SIAM J. Appl. Math. 74 (4) (2014), 11521173.
 (with H. Ibrahim)
Reduced ODE dynamics as formal relativistic asymptotics of a PeierlsNabarro model,
European Journal of Applied Mathematics 25 (4) (2014), 511529.
 (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 semiexplicit scheme for diagonal hyperbolic systems,
SIAM J. Numer. Anal. 52 (6) (2014), 27922814.
 (with A. Ghorbel)
Existence and nonexistence of semidiscrete shocks for a carfollowing model in traffic flow,
SIAM J. Math. Anal. 46 (6) (2014), 36123639.
 (with G. Costeseque, J.P. Lebacque)
A convergent scheme for HamiltonJacobi equations on a junction: application to traffic, Numer. Math. 129 (3) (2015), 405447.

The method of differential contractions, CRAS. 353 (2) (2015), 143147.
 (with E. Lindgren)
Pointwise regularity of the free boundary for the parabolic obstacle problem,
Calc. Var. 54 (1) (2015), 299347.
 (with Y. Noumir, A. Le Guilcher, N. Lardjane, A. Sarrazin)
(preprint version)
A fastmarching like algorithm for Geometrical Shock Dynamics,
J. Computational Physics 284 (2015), 206229.
 (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), 13461357.
 (with N. Forcadel, C. Imbert)
Steady state and long time convergence of spirals moving by forced mean curvature motion,
CPDE 40 (6) (2015), 11371181.
 (with G. Galise, C. Imbert)
A junction condition by specified homogenization,
Analysis and PDE 8 (8) (2015), 18911929.
 (with G. Chmaycem, M. Jazar)
A new contraction family for porous medium and fast diffusion equation,
ARMA 221 (2) (2016), 805815.
Preprints
 (with F. Murat and A. Sili) Error estimates
for the 3d1d dimension reduction in anisotropic heterogeneous linearized elasticity, (preliminary version, 2002).
 (with M. Al Haj)
Existence of traveling waves for Lipschitz discrete dynamics.
Monostable case as a limit of bistable cases, submitted.
 (with G. Chmaycem, M. Jazar)
Explicit phase diagram for a onedimensional blister model, submitted to ZAMM.
 (with C. Imbert)
Fluxlimited solutions for quasiconvex HamiltonJacobi equations on networks, preprint.
 (with C. Imbert)
Quasiconvex HamiltonJacobi equations posed on junctions: the multidimensional case, preprint.
 (with J. Alkhayal, S. Issa, M. Jazar)
Existence results for degenerate crossdiffusion systems with application to seawater intrusion, submitted.
 (with J. Alkhayal, M. Jazar)
Existence results for degenerate crossdiffusion systems with constraint: application to seawater intrusion in confined aquifer, submitted.