articles

Reaction-diffusion

Stability of travelling fronts in a model for flame propagation, Part I: Linear stability (with H. Berestycki and B. Larrouturou), Arch. Rat. Mech. Anal., 117 (1992), pp. 97-117.
Stability of travelling fronts in a model for flame propagation, Part II: Nonlinear stability, Arch. Rat. Mech. Anal., 117 (1992), pp. 119-153.
Convergence to travelling waves for solutions of a class of semilinear parabolic equations, J. Diff. Eq;, 108 (1994), pp. 262-295.
A parabolic equation of KPP type in higher dimensions (with J.F. Mallordy), SIAM J. Math. Anal., 27 (1995), pp. 1-20. lien
Eventual monotonicity and convergence to travelling fronts for the solutions of semilinear parabolic equations in cylinders, Ann. IHP, Analyse non linéaire, 14 (1997), pp. 499-552. lien
Stability of travelling waves in a model for conical flames in two space dimensions (with F. Hamel and R. Monneau). Ann. Sci. Ecole Norm. Sup. 37 (2004), pp. 469-506. lien
Existence and qualitative properties of bistable conical waves (with F. Hamel and R. Monneau). Discrete Contin. Dyn. Syst. A. 13 (2005), pp. 1069-1096. lien
Uniqueness and classification of travelling waves with Lipschitz level lines in bistable reaction-diffusion equations (with F. Hamel and R. Monneau). Discrete Contin. Dyn. Syst. A, 14 (2006), pp. 75-92. lien
Traveling waves with paraboloid like interfaces for balanced bistable dynamics (with X. Chen, H. Ninomiya, J.-S. Guo, F. Hamel), Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), pp. 369-393. lien
Nontrivial large-time behaviour in bistable reaction-diffusion equations (with V. Roussier), Annali Mat. Pura Appl., 188 (2009), pp. 207-233. lien
Stability of Generalized Transition Fronts (with A. Mellet, J. Nolen, L. Ryzhik.) Comm. Partial Diff. Eq., 34 (2009), pp. 521-552. lien
Existence of Generalized Transition Fronts in reaction-diffusion equations, (with A. Mellet and Y. Sire) Discret Cont. Dyn. Syst. A, 26 (2010), 303-312. lien
The periodic patch model for population dynamics with fractional diffusion (with H. Berestycki and L. Rossi), DCDS-S, 4 (2011), pp. 1-13. lien
Heteroclinic connections in multidimensional bistable reaction-diffusion equations (with F. Hamel), DCDS-S, 4 (2011), pp. 101-123. lien
Rate of attraction in a Fisher-KPP type model with shear flow (with P. Martinez), Comm. Pure Appl. Analysis, 11 (2012), pp. 2445-2472. lien
How travelling waves attract the solutions of KPP equations (with M. Bages and P. Martinez), Trans. Amer. Math. Soc, 364 (2012), pp. 5415-5468. lien
Existence and nonexistence of Fisher-KPP transition fronts (with J. Nolen, L. Ryzhik, A. Zlatos), Arch. Rat. Mech. Anal., 203 (2012), pp. 217-246. lien
Transition between exponential and linear propagation in Fisher-KPP type reaction-diffusion equations (with A.-C. Coulon), Comm. Partial Differential Equations 37 (2012), pp. 2029-2049. lien
Existence and asymptotics of fronts in nonlocal combustion models (w. A. Mellet and Y. Sire), Comm. Pure Appl. Analysis, lien
The influence of fractional diffusion on Fisher-KPP equations (with X. Cabré), Comm. Math. Phys. 320 (2013), pp. 679-22. ArXiv preprint.
Propagation in Fisher-KPP type equations with fractional diffusion in periodic media (with X. Cabré and A.-C. Coulon), C. R. Math. Acad. Sci. Paris 350 (2012), pp. 885-890. lien
The influence of a line of fast diffusion in Fisher-KPP propagation (with H. Berestycki and L. Rossi), J. Math. Biol. 66 (2013), pp. 743-766. lien
Fisher-KPP propagation in the presence of a line: further effects (with H. Berestycki and L. Rossi), to appear in Nonlinearity. lien
A short proof of the logarithmic Bramson correction in Fisher-KPP equations (with F. Hamel, J. Nolen, L. Ryzhik), to appear in Networks Heterog. Media. lien
The logarithmic time delay of KPP fronts in a periodic medium (with F. Hamel, J. Nolen, L. Ryzhik), to appear in J. European Math. Society. lien
Power-like delays in Fisher-KPP type equations (with J. Nolen and L. Ryzhik), to appear in Comm. Partial Diff. Equations. lien
The effect of a line with nonlocal diffusion on Fisher-KPP propagation (with H. Berestycki, A.-C. Coulon, L. Rossi), M3AS, to appear. lien
Gradient estimates and symmetrization for Fisher-KPP front propagation with fractional diffusion (with A. Tarfulea), preprint. lien

Hamilton-Jacobi

Convergence to periodic fronts in semilinear parabolic equations (with G. Namah), Nonlinear Diff. Eq. Appl., 4 (1997), pp. 521-536. lien
Comportement asymptotique des solutions d'équations de Hamilton-Jacobi monodimensionnelles, C. R. Acad. Sci. Paris, t. 326, Série I, pp. 185-189, 1998.
Remarks on the time-asymptotic behaviour of the solutions of Hamilton-Jacobi equations (with G. Namah), Comm. Partial Diff. Eq., 24 (1999), pp. 883-889. lien
The 'hump' effect in solid propellant combustion (with G. Namah), Interfaces Free Bound. 2 (2000), pp. 449-467. lien
Convergence to steady states or periodic solutions in a class of Hamilton-Jacobi equations, J. Math. Pures Appl., 80 (2001), pp. 85-104. lien
Large time behaviour of fronts governed by eikonal equations (with G. Barles). Interfaces Free Bound. 5 (2003), pp. 83-102.
Time-asymptotic behaviour in time-periodic Hamilton-Jacobi equations on the circle (with P. Bernard). Comm. Partial Differential Equations 29 (2004), pp. 457-469. lien
Ergodic type problems and large time behaviour of unbounded solutions of Hamilton-Jacobi equations. (with G. Barles), Comm. Partial Differential Equations 31 (2006), pp. 1209-1225. lien
Large-time convergence in Hamilton-Jacobi equations; proceedings of the CSTNA2005 wokshop 'Control and Numerics'. lien
Propriétés qualitatives des solutions de viscosité des équations d'Hamilton-Jacobi (d'après Fathi, Siconolfi, Bernard), actes du Séminaire Bourbaki, 2007. lien
A class of Hamilton-Jacobi equations with constraint: uniqueness and constructive approach (with S. Mirrahimi), to appear. lien

Applied dynamical systems

Mathematical analysis of a planar flame model with nonlinear diffusion, Nonlinear Analysis, TMA, 21 (1993), pp. 745-761.
Global stability and convergence to wave trains in monotone parabolic systems (with D. Terman and V.A. Volpert), SIAM J. Math. Anal., 27 (1996), pp. 1261-1269.
Bifurcations of travelling waves in the thermo-diffusive model for flame propagation (with L. Glangetas), Arch. Rat. Mech. Anal., 134 (1996), pp. 341-402. lien
Stability of travelling waves in a parabolic equations with discontinuous source term (with C.-M. Brauner and C. Schmidt-Lainé); Comm. Nonlinear Appl. Anal., 1 (1995), pp. 987-1000.
A threshold phenomenon arising in the propagation of a spherical flame (with J. Audounet and V. Giovangigli), Physica D, 121 (1998), pp. 295-316. lien
Existence and stability of travelling waves in a kinetic model for two-phase flows (with K. Domelevo), Comm. Partial Diff. Eq., 1 (1999), pp. 61-109. lien
Stability of strong ZND waves in the Majda detonation models (with J.-P. Vila), Asymptotic Analysis, 18 (1998), pp. 329-348. lien
A kinetic equation describing the dynamics of dense sparays (with P. Villedieu), Math. Models Methods Appl. Sci. 11 (2001), pp. 867-882. lien
Ignition and propagation in an integro-differential model for spherical flames (with J.-L. Vàzquez); Discrete Contin. Dyn. Syst. Ser. B, 2 (2002), pp. 379-387.
Numerical simulations of a point-source initiated flame ball with heat losses (with J. Audounet and H. Rouzaud), Math. Model. Numer. Anal. 36 (2002), pp. 273-291.
Mathematical derivation of a nonlinear integro-differential equation for the radius of a spherical flame (with C. Lederman and N. Wolanski). Ann. Mat. Pura Appl. 183 (2004), pp. 173-239. lien
Large time behaviour of the solutions to a one-dimensional Stefan problem with a kinetic conditions at the free boundary (with D. Hilhorst and F. Issard-Roch). European J. Appl. Math. 15 (2004), pp. 297-313.
Existence of pulsating waves in a model of flames in sprays (with P. Constantin, K. Domelevo, L. Ryzhik) J. Eur. Math. Soc. 8 (2006), pp. 555-584. lien
Existence and stability of time-periodic solutions in a model for spherical flames with time-periodic heat losses (with H. Rouzaud), J. Comput. Appl. Math. 190 (2006), pp. 376-392. lien
Propagation and quenching in a reactive Burgers-Boussinesq system (with P. Constantin, L. Ryzhik and N. Vladimirova), Nonlinearity 21 (2008), pp. 221-271. lien
Relaxation rate in thermo-diffusive models with strongly varying diffusion scale (with P. Clavin and L. Masse), Comm. Math. Sciences, 9 (2011), pp. 127-141. lien
Traveling wave solutions of advection-diffusion equations with nonlinear diffusion (with L. Monsaingeon and A. Novikov), Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), pp. 705-735. lien

Free boundary problems

A nonlinear oblique derivative problem for the heat equation, Part 1: Basic results (with F. Méhats), Ann. IHP, Analyse non linéaire 16 (1999), pp. 221-253. lien
A nonlinear oblique derivative problem for the heat equation, Part 2: Singular self-similar solutions (with F. Méhats), Ann. IHP, Analyse non linéaire, 16 (1999), pp. 691-724. lien
A nonlinear oblique derivative problem for the heat equation: analogy with the porous medium equation (with L. Caffarelli), Ann. IHP, Analyse non linéaire, 19 (2002), pp. 41-80. lien
Uniform Hölder estimates in a class of elliptic systems and applications to singular limits in models for diffusion flames (with L. Caffarelli), Arch. Ration. Mech. Anal. 183 (2007), pp. 457-487. lien
Variational problems with free boundaries for the fractional Laplacian (with L. Caffarelli and Y. Sire). J. European Math. Soc., 12 (2010), pp. 1151-1179. lien
Nonlocal minimal surfaces (with L. Caffarelli and O. Savin). Comm. Pure Appl. Math., 63 (2010), pp. 1111-1144. lien
Regularity in a one-phase free boundary problem for the fractional Laplacian (with D. DeSilva), Ann. IHP, Analyse Non Linéaire 29 (2012), pp. 335-367. lien
Travelling graphs for the forced mean curvature motion in an arbitrary space dimension (with R. Monneau et V. Roussier), to appear in Ann. Sci. ENS. lien

Notes aux Comptes-Rendus de l'Académie des Sciences

Etude mathématique d'un modèle de flamme plane, C.R. Acad. Sci. Paris, t. 311, Série I, pp. 593-596, 1990.
Stabilité d'ondes progressives dans un modèle de flamme plissée (with H. Berestycki and B.Larrouturou, C.R. Acad. Sci. Paris, t. 311, Série I, pp. 769-774, 1990.
Comportement asymptotique des solutions d'une équation parabolique de type KPP en dimension supérieure (with J.-F. Mallordy), C.R. Acad. Sci. Paris, t. 311, Série I, pp.pp. 817-820, 1992.
Comportement asymptotique des solutions d'une classe d'équations paraboliques semiliéaires, C.R. Acad. Sci. Paris, t. 316, Série I, pp. 461-464, 1993.
Bifurcations d'ondes progressives dans un modèle de flamme (with L. Glangetas), C.R. Acad. Sci. Paris, t. 318, Série I, pp. 389-393, 1994.
Un problème de dérivées obliques non linéaire pour l'équation de la chaleur (with F. Méhats), C.R. Acad. Sci. Paris, t. 321, Série I, pp. 1319-1322, 1995.
Existence and stabilité d'ondes progrssives dans un modèle cinétique diphasique (with K. Domelevo), C.R. Acad. Sci. Paris, t. 324, Série I, pp. 371-376, 1997.
Comportement asymptotique des solutions d'une classe d'équations paraboliques et de Hamilton-Jacobi (with G. Namah), C.R. Acad. Sci. Paris, t. 324, Série I, pp. 1367-1370,1997.
Mathematical justification of a nonlinear integro-differential equation for the propagation of a spherical flame (with C. Lederman and N. Wolanski), C. R. Acad. Sci. Paris, Sér. I, 334 (2002), pp. 569-574. lien
Existence et propriétés qualitatives de fronts coniques bistables en dimension 2 d'espace (with F. Hamel and R. Monneau). C. R. Math. Acad. Sci. Paris 339 (2004), pp. 699-704.
Dynamique en grand temps pour une classe d'équations de type KPP en milieu périodique (with M. Bages and P. Martinez), C.R. Acad. Sci. Paris, 346 (2008), pp. 1051-1056. lien
Propagation de fronts dans les équations de Fisher-KPP with diffusion fractionnaire (with X. Cabré), C.R. Acad. Sci. Paris, 347 (2009), pp. 1361-1366. lien