François Hamel

Professor Institut Universitaire de France Université d'Aix-Marseille LATP Faculté des Sciences 39 rue Frédéric Joliot-Curie 13453 Marseille Cedex 13, France Phone : + 33 4 91 28 86 94 francois.hamel@univ-amu.fr

Research fields

Elliptic and parabolic non-linear partial differential equations
Traveling waves, propagation phenomena, pulsating fronts in periodic media, generalized transition waves
Degenerate equations, singular limits, free boundary problems
Qualitative properties, classification of solutions of elliptic or parabolic equations, inverse problems
Shape and eigenvalue optimization problems
Population dynamics, ecology, combustion

Vitae

Member of the Institut Universitaire de France

Chair of the Applied Analysis team in LATP from 2006 until 2010

Fellow of the Alexander von Humboldt Foundation, 2008-2010

Professor, Aix-Marseille University, since 2001

From 1995 until 2001, I had a CNRS research position at Laboratoire Jacques-Louis Lions, Université Paris VI

During the year 1997-1998, I was Lecturer of Mathematics at the Department of Mathematics of MIT

I graduated from the Ecole Normale Supérieure in Paris

Publications

(with N. Nadirashvili and Y. Sire) Convexity of level sets for elliptic problems in convex domains or convex rings: two counterexamples. (arxiv)

Bistable transition fronts in R^N. (arxiv)

(with J. Nolen, J.-M. Roquejoffre and L. Ryzhik) The logarithmic delay of KPP fronts in a periodic medium. (arxiv)

(with A. Zlatos) Speed-up of combustion fronts in shear flows, Math. Ann., forthcoming. (pdf)

(with O. Bonnefon, J. Garnier and L. Roques) Inside dynamics of delayed traveling waves, Math. Model. Nat. Phenom., forthcoming. (pdf)

(with N. Nadirashvili and E. Russ) Symmetrization of functions and principal eigenvalues of elliptic operators, Semin. Equ. Deriv. Partielles, Ecole Polytechnique, forthcoming. (pdf)

(with A. Zlatos) The Harnack inequality for a class of degenerate elliptic operators, Int. Math. Res. Notices, forthcoming. (pdf)

(with J. Nolen, J.-M. Roquejoffre and L. Ryzhik) A short proof of the logarithmic Bramson correction in Fisher-KPP equations, Netw. Heterog. Media 8 (2013), 275-289. (pdf)

(with J. Garnier, T. Giletti and L. Roques) Inside dynamics of pulled and pushed fronts, J. Math. Pures Appl. 98 (2012), 428-449. (pdf)

(with L. Roques, J. Garnier and E. Klein) Allee effect promotes diversity in traveling waves of colonization, Proc. Nat. Acad. Sci. 109 (2012), 8828-8833.

(with J.-S. Guo) Propagation and blocking in periodically hostile environments, Arch. Ration. Mech. Anal. 204 (2012), 945-975. (pdf)

(with H. Berestycki) Generalized transition waves and their properties, Comm. Pure Appl. Math. 65 (2012), 592-648. (pdf)

(with G. Nadin) Spreading properties and complex dynamics for monostable reaction-diffusion equations, Comm. Part. Diff. Equations 37 (2012), 511-537. (pdf)

(with J. Garnier and L. Roques) Success rate of a biological invasion in terms of the spatial distribution of the founding population, Bull. Math. Biol. 74 (2012), 453-473. (pdf)

(with M. Cristofol, J. Garnier and and L. Roques) Uniqueness from pointwise observations in a multi-parameter inverse problem, Comm. Pure Appl. Anal. 11 (2012), 173-188. (pdf)

(with G. Nadin and L. Roques) A viscosity solution method for the spreading speed formula in slowly varying media, Indiana Univ. Math. J. 60 (2011), 1229-1247. (pdf)

(with N. Nadirashvili and E. Russ) Rearrangement inequalities and applications to isoperimetric problems for eigenvalues, Annals of Math. 174 (2011), 647-755. (pdf)

(with M. Efendiev) Asymptotic behavior of solutions of semilinear elliptic equations in unbounded domains: two approaches, Adv. Math. 228 (2011), 1237-1261. (pdf)

(with M. El Smaily and R. Huang) Two-dimensional curved fronts in a periodic shear flow, Nonlinear Analysis 74 (2011), 6469-6486. (pdf)

(with L. Roques) Uniqueness and stability properties of monostable pulsating fronts, J. European Math. Soc. 13 (2011), 345-390. (pdf)

 (with J.-M. Roquejoffre) Heteroclinic connections for multidimensional bistable reaction-diffusion equations, Disc. Cont. Dyn. Systems S 4 (2011), 101-123. (pdf)

(with Y. Sire) Spreading speeds for some reaction-diffusion equations with general initial conditions, SIAM J. Math. Anal. 42 (2010), 2872-2911. (pdf)

(with L. Roques) Fast propagation for KPP equations with slowly decaying initial conditions, J. Diff. Equations 249 (2010), 1726-1745. (pdf)

(with J. Fayard and L. Roques) Spreading speeds in slowly oscillating environments, Bull. Math. Biol. 72 (2010), 1166-1191. (pdf)

(with L. Ryzhik) Travelling waves for the thermodiffusive system with arbitrary Lewis numbers, Arch. Ration. Mech. Anal. 195 (2010), 923-952. (pdf)

(with H. Berestycki and N. Nadirashvili) The speed of propagation for KPP type problems. II - General domains, J. Amer. Math. Soc. 23 (2010), 1-34. (pdf)

(with L. Roques, J. Fayard, B. Fady and E.K. Klein) Recolonisation by diffusion can generate increasing rates of spread, Theor. Popul. Biol. 77 (2010), 205-212. (pdf)

(with N. Nadirashvili) Extinction versus persistence in strong oscillating flows, Arch. Ration. Mech. Anal. 195 (2010), 205-223. (pdf)

(with H. Berestycki and H. Matano) Bistable travelling waves around an obstacle, Comm. Pure Appl. Math. 62 (2009), 729-788. (pdf)

(with M. El Smaily and L. Roques) Homogenization and influence of fragmentation in a biological invasion model, Disc. Cont. Dyn. Systems A 25 (2009), 321-342. (pdf)

(with H. Berestycki and G. Nadin) Asymptotic spreading in heterogeneous diffusive media, J. Funct. Anal. 255 (2008), 2146-2189. (pdf)

Qualitative properties of monostable pulsating fronts : exponential decay and monotonicity, J. Math. Pures Appl. 89 (2008), 355-399. (pdf)

(with L. Roques) Mathematical analysis of the optimal habitat configurations for species persistence, Math. Biosciences 210 (2007), 34-59. (pdf)

(with H. Berestycki) Generalized travelling waves for reaction-diffusion equations, In: Perspectives in Nonlinear Partial Differential Equations. In honor of H. Brezis, Contemp. Math. 446, Amer. Math. Soc., 101-123. (pdf)

(with N. Nadirashvili and E. Russ) Some isoperimetric problems for the principal eigenvalues of second-order elliptic operators in divergence form, C.R. Acad. Sci. Paris Ser. I 344 (2007), 169-174.

(with X. Chen, J.-S. Guo, H. Ninomiya and J.-M. Roquejoffre) Traveling waves with paraboloid like interfaces for balanced bistable dynamics, Ann. Institut H. Poincaré, Analyse Non Linéaire 24 (2007), 369-393. (pdf)

(with H. Berestycki and L. Rossi) Liouville type results for semilinear elliptic equations in unbounded domains, Annali Mat. Pura Appl. 186 (2007), 469-507. (pdf)

(with H. Berestycki) Fronts and invasions in general domains, C.R. Acad. Sci. Paris Ser. I 343 (2006), 711-716.

(with J.-S. Guo) Front propagation for discrete periodic monostable equations, Math. Ann. 335 (2006), 489-525. (pdf)

(with R. Monneau and J.-M. Roquejoffre) Asymptotic properties and classification of bistable fronts with Lipschitz level sets, Disc. Cont. Dyn. Systems A 14 (2006), 75-92. (pdf)

(with L. Ryzhik) Non-adiabatic KPP fronts with an arbitrary Lewis number, Nonlinearity 18 (2005), 2881-2902. (pdf)

(with H. Berestycki, A. Kiselev and L. Ryzhik) Quenching and propagation in KPP reaction-diffusion equations with a heat loss, Arch. Ration. Mech. Anal. 178 (2005), 57-80. (pdf)

(with R. Monneau and J.-M. Roquejoffre) Existence and qualitative properties of multidimensional conical bistable fronts, Disc. Cont. Dyn. Systems A 13 (2005), 1069-1096. (pdf)

(with H. Berestycki and L. Roques) Analysis of the periodically fragmented environment model : II - Biological invasions and pulsating travelling fronts, J. Math. Pures Appl. 84 (2005), 1101-1146. (pdf)

(with H. Berestycki and N. Nadirashvili) The speed of propagation for KPP type problems. I - Periodic framework, J. European Math. Soc. 7 (2005), 173-213. (pdf)

(with N. Nadirashvili and E. Russ) An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift, C.R. Acad. Sci. Paris Ser. I 340 (2005), 347-352.

(with H. Berestycki and L. Roques) Analysis of the periodically fragmented environment model : I - Species persistence, J. Math. Biol. 51 (2005), 75-113. (pdf)

Propagation phenomena for KPP-type equations in unbounded domains, In: Proceedings Equadiff 03, International Conference on Differential Equations, F. Dumortier, H. W. Broer, J. Mawhin, A. Vanderbauwhede, S. Verduyn Lunel eds., World Scientific Publ., Singapore, 2005, 789-794.

(with H. Berestycki) Gradient estimates for elliptic regularizations of semilinear parabolic and degenerate elliptic equations, Comm. Part. Diff. Equations 30 (2005), 139-156. (pdf)

(with H. Berestycki and N. Nadirashvili) Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena, Comm. Math. Phys. 253 (2005), 451-480. (pdf)

(with R. Monneau and J.-M. Roquejoffre) Existence et propriétés qualitatives de fronts coniques bistables en dimension 2 d'espace, C.R. Acad. Sci. Paris Ser. I 339 (2004), 699-704.

(with H. Berestycki and L. Roques) Equations de réaction-diffusion et modèles d'invasions biologiques dans les milieux périodiques, C.R. Acad. Sci. Paris Ser. I 339 (2004), 549-554.

(with R. Monneau and J.-M. Roquejoffre) Stability of conical fronts in a combustion model, Ann. Scient. Ecole Norm. Sup. 37 (2004), 469-506. (pdf)

(with H. Berestycki and N. Nadirashvili) Propagation speed for reaction-diffusion equations in general domains, C.R. Acad. Sci. Paris Ser. I 339 (2004), 163-168.

Conical-shaped travelling fronts in some reaction-diffusion equations, In: Proc. Conference on ``Dynamic patterns in reaction-diffusion systems and the related topics'' (Kyoto 2002), Res. Inst. Math. Sci. Kyoto Univ., 2003, 25-39.

(with R. Monneau) Conical-shaped travelling fronts applied to the mathematical analysis of the shape of premixed Bunsen flames, In: Nonlinear PDE's in Condensed Matter and Reactive Flows, H. Berestycki and Y. Pomeau eds., Kluwer Academic Publ., 2002, 169-187. (pdf)

(with H. Berestycki) Front propagation in periodic excitable media, Comm. Pure Appl. Math. 55 (2002), 949-1032. (pdf)

(with R. Monneau) Existence and uniqueness of solutions of a conical-shaped free boundary problem in R^2. Interf. Free Boundaries 4 (2002), 167-210. (pdf)

(with N. Nadirashvili) Travelling fronts and entire solutions of the Fisher-KPP equation in R^N, Arch. Ration. Mech. Anal. 157 (2001), 91-163. (pdf)

Some existence, monotonicity and uniqueness results for pulsating travelling fronts in periodic media and periodic domains, In: Proc. International Conference on "Interfaces, Pulses and Waves in Nonlinear Dissipative Systems" (Kyoto 2000), R.I.M.S. Project 2000 ``Reaction-diffusion systems: theory and applications'', Res. Inst. Math. Sci. Kyoto Univ., 2001, 29-42.

(with A. Blouza and F. Coquel) Reduction of linear kinetic systems with multiple scales, Comb. Theory Model. 4 (2000), 339-362. (pdf)

(with H. Berestycki and R. Monneau) One-dimensional symmetry of bounded entire solutions of some elliptic equations, Duke Math. J. 103 (2000), 375-396. (pdf)

(with R. Monneau) Solutions of semilinear elliptic equations in R^N with conical-shaped level sets, Comm. Part. Diff. Equations 25 (2000), 769-819. (pdf)

(with H. Berestycki) Non-existence of travelling fronts solutions for some bistable reaction-diffusion equations, Adv. Diff. Equations 5 (2000), 723-746. (pdf)

(with S. Omrani) Existence of multidimensional travelling fronts with a multistable nonlinearity, Adv. Diff. Equations 5 (2000), 557-582. (pdf)

(with A. Bonnet) Existence of non-planar solutions of a simple model of premixed Bunsen flames, SIAM J. Math. Anal. 31 (1999), 80-118. (pdf)

Formules min-max pour les vitesses d'ondes progressives multidimensionnelles, Ann. Fac. Sci. Toulouse 8 (1999), 259-280. (pdf)

(with N. Nadirashvili) Entire solutions of the KPP equation, Comm. Pure Appl. Math. 52 (1999), 1255-1276. (pdf)

(with A. Blouza and F. Coquel) Réduction algorithmique de systèmes cinétiques raides, C.R. Acad. Sci. Paris Ser. I 327 (1998), 979-984.

(with A. Blouza and F. Coquel) Algorithmic and systematic reduction of a class of kinetic networks, Proceedings of the International Conference on Air Pollution Modelling and Simulation, APMS'98, CERMICS-INRIA (1998).

(with R. Monneau) Solutions d'équations elliptiques semilinéaires dans R^N ayant des courbes de niveau de forme conique, C.R. Acad. Sci. Paris Ser. I 327 (1998), 645-650.

(with N. Nadirashvili) Existence et propriétés qualitatives de solutions entières de l'équation de KPP, C.R. Acad. Sci. Paris Ser. I 327 (1998), 479-484.

Reaction-diffusion problems in cylinders with no invariance by translation, Part II: Monotone perturbations, Ann. Inst. H. Poincaré, Anal. Non Linéaire 14 (1997), 555-596. (pdf)

Reaction-diffusion problems in cylinders with no invariance by translation, Part I: Small perturbations, Ann. Inst. H. Poincaré, Anal. Non Linéaire 14 (1997), 457-498. (pdf)

Problèmes de réaction-diffusion sans invariance par translation dans des cylindres infinis, C.R. Acad. Sci. Paris Ser. I 321 (1995), 855-860.

(with S. Omrani) Existence de fronts progressifs pour un problème elliptique avec un terme non linéaire de type multistable, C.R. Acad. Sci. Paris Ser. I 321 (1995), 419-424.

(with H. Berestycki) Non-existence de fronts progressifs pour une équation de réaction-diffusion de type "bistable", C.R. Acad. Sci. Paris Ser. I 321 (1995), 287-292.