François Hamel
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Professor Institut de Mathématiques de Marseille Site de Saint-Charles, 3 place Victor Hugo, Case 19 13331 Marseille Cedex 3, France Phone : + 33 4 13 55 14 61 francois.hamel@univ-amu.fr |
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Short Vitae
Head of the Applied Analysis group in I2M, 2024-
Director of Archimede LabEx, 2014-2019
Principal investigator of the ANR project NONLOCAL, 2014-2019
Inclusion in the list of Highly Cited Researchers, 2014
Visiting positions at the University of California, Berkeley, and Stanford University, 2013
Member of the Institut Universitaire de France, 2009-2014
Fellow of the Alexander von Humboldt Foundation, 2008-2010
Head of the Applied Analysis team in LATP, 2006-2010
Professor, Aix-Marseille Université, since 2001
Lecturer of Mathematics at the Department of Mathematics of MIT, 1997-1998
CNRS research position at Laboratoire Jacques-Louis Lions, Sorbonne Université, 1995-2001
I graduated from the Ecole Normale Supérieure in Paris
Research fields
Elliptic and parabolic non-linear partial differential
equations
Traveling
waves, propagation phenomena, pulsating fronts in periodic media, generalized
transition waves
Qualitative
properties, classification of solutions of elliptic or parabolic equations, inverse problems
Degenerate
equations, singular limits, free boundary problems
Shape and
eigenvalue optimization problems
Population
dynamics, ecology, combustion
Publications
(with E. Russ) A Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition. (pdf)
(with A. Karakhanyan) Potential flows away from stagnation in infinite cylinders. (pdf)
(with M. Zhang) KPP transition fronts in a one-dimensional two-patch habitat. (pdf)
(with L. Rossi) Spreading, flattening and logarithmic lag for reaction-diffusion equations in R^N: old and new results. (pdf)
(with L. Rossi) Spreading speeds and spreading sets of reaction-diffusion equations. (pdf)
(with W. Ding and X. Liang) Bistable pulsating fronts in slowly oscillating environments. (pdf)
(with L. Rossi) Asymptotic one-dimensional symmetry for the Fisher-KPP equation, J. Europ. Math. Soc., forthcoming. (pdf)
(with M. Alfaro and L. Roques) Propagation or extinction in bistable equations: the non-monotone role of initial fragmentation, Disc. Cont. Dyn. Systems S, Special Issue in Honor of Yihong Du 17 (2024), 1460-1484. (pdf)
(with F. Lutscher and M. Zhang) Propagation phenomena in periodic patchy landscapes with interface conditions, J. Dyn. Diff. Equations 36 (2024), 435-486. (pdf)
(with M. Alfaro, F. Patout and L. Roques) Adaptation in a heterogeneous environment II: To be three or not to be, J. Math. Biol. 87 (2023), 68. (pdf)
(with N. Nadirashvili) Circular flows for the Euler equations in two-dimensional annular domains, and related free boundary problems, J. Europ. Math. Soc. 25 (2023), 323-368. (pdf)
(with J.-S. Guo and C.-C. Wu) Forced waves for a three-species predator-prey system with nonlocal dispersal in a shifting environment, J. Diff. Equations 345 (2023), 485-518. (pdf)
(with M. Zhang) Reaction-diffusion fronts in funnel-shaped domains, Adv. Math. 412 (2023), 108807. (pdf)
(with F. Lutscher and M. Zhang) Propagation and blocking in a two-patch reaction-diffusion model, J. Math. Pures Appl. 168 (2022), 213-267. (pdf)
(with H. Ninomiya) Localized and expanding entire solutions of reaction-diffusion equations, J. Dyn. Diff. Equations 34 (2022), 2937-2974. (pdf)
(with G. Nadin) Diameters of the level sets for reaction-diffusion equations in nonperiodic slowly varying media, Proc. Amer. Math. Soc. 150 (2022), 3549-3564. (pdf)
(with L. Rossi) Spreading sets and one-dimensional symmetry for reaction-diffusion equations, Séminaire Laurent Schwartz EDP Applications (2021-2022), exp. XI, 25 p. (pdf)
(with M. Alfaro, L. Girardin and L. Roques) When the Allee threshold is an evolutionary trait: persistence vs. extinction, J. Math. Pures Appl. 155 (2021), 155-191. (pdf)
(with F. Lavigne and L. Roques) Adaptation in a heterogeneous environment, I: Persistence versus extinction, J. Math. Biol. 83 (2021), 14. (pdf)
(with Y. Liu, P. Sicbaldi, K. Wang and J. Wei) Half-space theorems for the Allen-Cahn equation and related problems, J. reine angew. Math. (Crelle's J.) 770 (2021), 113-133. (pdf)
(with F. Lavigne, G. Martin and L. Roques) Dynamics of adaptation in an anisotropic phenotype-fitness landscape, Nonlinear Analysis, Real World Appl. 54 (2020), 103107. (pdf)
(with H. Guo and W.-J. Sheng) On the mean speed of bistable transition fronts in unbounded domains, J. Math. Pures Appl. 136 (2020), 92-157. (pdf)
(with J. Coville) On generalized principal eigenvalues of nonlocal operators with a drift, Nonlinear Analysis 193 (2020), 111569. (pdf)
(with C. Henderson) Propagation in a Fisher-KPP equation with non-local advection, J. Funct. Anal. 278 (2020), 108426. (pdf)
(with N. Nadirashvili and Y. Sire) Geometric properties of superlevel sets of semilinear elliptic equations in convex domains, 2018 MATRIX Annals, J. de Gier et al. (eds), Springer Nature (2020), 249-263.
(with M.-E. Gil, G. Martin and L. Roques) Dynamics of fitness distributions in the presence
of a phenotypic optimum: an integro-differential approach, Nonlinearity 32 (2019), 3485-3522. (pdf)
(with J. Brasseur, J. Coville and E. Valdinoci) Liouville type results for a nonlocal obstacle problem, Proc. London Math. Soc. 119 (2019), 291-328. (pdf)
(with N. Nadirashvili) A Liouville theorem for the Euler equations in the plane, Arch. Ration. Mech. Anal. 233 (2019), 599-642. (pdf)
(with L. Rossi and E. Russ) Optimization of some eigenvalue problems with large drift, Comm. Part. Diff. Equations 43 (2018), 945-964. (pdf)
(with E. Grenier) Large time monotonicity of solutions of reaction-diffusion equations in R^N, J. Math. Pures Appl. 112 (2018), 89-117. (pdf)
(with N. Nadirashvili) Parallel and circular flows for the two-dimensional Euler equations, Séminaire Laurent Schwartz EDP Applications (2017-2018), exp. V, 1-13. (pdf)
(with M.-E. Gil, G. Martin and L. Roques) Mathematical properties of a class of integro-differential models from population genetics, SIAM J. Appl. Math. 77 (2017), 1536-1561. (pdf)
(with W. Ding and X. Zhao) Bistable pulsating fronts for reaction-diffusion equations in a periodic habitat, Indiana Univ. Math. J. 66 (2017), 1189-1265. (pdf)
(with Y.-Y. Chen and J.-S. Guo) Traveling waves for a lattice dynamical system arising in a diffusive endemic model, Nonlinearity 30 (2017), 2334-2359. (pdf)
(with X. Ros-Oton, Y. Sire and E. Valdinoci) A one-dimensional symmetry result for a class of nonlocal semilinear equations in the plane, Ann. Institut H. Poincaré, Analyse Non Linéaire 34 (2017), 469-482. (pdf)
(with D. Bonheure) One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in R^N, Chin. Ann. Math. Special Issue in Honor of Haim Brezis 38B (2017), 149-172. (pdf)
(with N. Nadirashvili) Shear flows of an ideal fluid and elliptic equations in unbounded domains, Comm. Pure Appl. Math. 70 (2017), 590-608. (pdf)
(with E. Russ) Comparison results and improved quantified inequalities for semilinear elliptic equations, Math. Ann. 367 (2017), 311-372. (pdf)
(with T. Giletti) Sharp thresholds between finite spread and uniform convergence for a reaction-diffusion equation with oscillating initial data, J. Diff. Equations 262 (2017), 1461-1498. (pdf)
(with J. Garnier and L. Roques) Transition fronts and stretching phenomena for a general class of reaction-dispersion equations, Disc. Cont. Dyn. Syst. 37 (2017), 743-756. (pdf)
(with H. Guo) Monotonicity of bistable transition fronts in R^N, J. Elliptic Parabol. Equ. 2 (2016), 145-155. (pdf)
(with L. Rossi) Transition fronts for the Fisher-KPP equation, Trans. Amer. Math. Soc. 368 (2016), 8675-8713. (pdf)
(with N. Nadirashvili and Y. Sire) Convexity of level sets for elliptic problems in convex domains or convex rings: two counterexamples, Amer. J. Math. 138 (2016), 499-527. (pdf)
(with J. Nolen, J.-M. Roquejoffre and L. Ryzhik) The logarithmic delay of KPP fronts in a periodic medium, J. Europ. Math. Soc. 18 (2016), 465-505. (pdf)
Bistable transition fronts in R^N, Adv. Math. 289 (2016), 279-344. (pdf)
(with E. Russ) Comparaisons et inégalités améliorées pour des équations elliptiques semi-linéaires, Equations aux dérivées partielles et leurs applications, Actes du colloque Edp-Normandie, Le Havre 2015, Fédération Normandie-Mathématiques (2016), 465-505.
(with W. Ding and X. Zhao) Transition fronts for periodic bistable reaction-diffusion equations, Calc. Var. Part. Diff. Equations 54 (2015), 2517-2551. (pdf)
(with L. Rossi) Admissible speeds of transition fronts for non-autonomous monostable equations, SIAM J. Math. Anal. 47 (2015), 3342-3392. (pdf)
(with O. Bonnefon, J. Coville, J. Garnier and L. Roques) The spatio-temporal dynamics of neutral genetic diversity, Ecological Complexity 20 (2014), 282-292. (pdf)
(with L. Ryzhik) On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds, Nonlinearity 27 (2014), 2735-2753. (pdf)
(with L. Roques) Persistence and propagation in periodic reaction-diffusion models, Tamkang J. Math. 45 (2014), 217-228. (pdf)
(with A. Zlatos) The Harnack inequality for a class of degenerate elliptic operators, Int. Math. Res. Notices 2013 (2013), 3732-3743. (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 O. Bonnefon, J. Garnier and L. Roques) Inside dynamics of delayed traveling waves, Math. Model. Nat. Phenom. 8 (2013), 42-59. (pdf)
(with A. Zlatos) Speed-up of combustion fronts in shear flows, Math. Ann. 356 (2013), 845-867. (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 J.-S. Guo) Propagation and blocking in periodically hostile environments, Arch. Ration. Mech. Anal. 204 (2012), 945-975. (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 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 N. Nadirashvili and E. Russ) Symmetrization of functions and principal eigenvalues of elliptic operators, Séminaire Laurent Schwartz EDP Applications (2011-2012), exp. XXIV, 1-15. (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. (2007), 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.