Propagation phenomena and nonlocal equations









Coordinator and head of partner 1: François Hamel (Université d'Aix-Marseille)

Head of partner 2: Henri Berestycki (EHESS)

ANR project NONLOCAL (Propagation phenomena and nonlocal equations)  





 Henri Berestycki (EHESS)

 Julien Berestycki (on secondment from Université Pierre et Marie Curie Paris VI)

 Olivier Bonnefon (INRA Avignon)

 Julien Brasseur (PhD student, Université d'Aix-Marseille and INRA Avignon)

 Cécile Carrère (PhD student, Université d'Aix-Marseille)

 Nicolas Champagnat (INRIA Nancy)

 Guillemette Chapuisat (Université d'Aix-Marseille)

 Benjamin Contri (former PhD student, Université d'Aix-Marseille)

 Anne-Charline Coulon (former PhD student, Université Paul Sabatier Toulouse III)

 Jérôme Coville (INRA Avignon)

 Laurent Dietrich (former PhD student, Université Paul Sabatier Toulouse III)

 Weiwei Ding (former PhD student, Université d'Aix-Marseille)

 Romain Ducasse (PhD student, EHESS)

 Grégory Faye (CNRS, Université Paul Sabatier Toulouse III)

 Joseph Feneuil (former PhD student, Université Grenoble Alpes)

 Jimmy Garnier (CNRS, Université Savoie Mont-Blanc)

 Marie-Ève Gil (PhD student, Université d'Aix-Marseille and INRA Avignon)

 Thomas Giletti (Université de Lorraine)

 Léo Girardin (PhD student, Université Pierre et Marie Curie Paris VI)

 François Hamel (Université d'Aix-Marseille)

 Louis Jeanjean (Université de Franche-Comté)

 Elisabeth Logak (Université de Cergy-Pontoise)

 Jonathan Martin (former post-doctoral fellow, Université d'Aix-Marseille)

 Patrick Martinez (Université Paul Sabatier Toulouse III)

 Grégoire Nadin (CNRS, Université Pierre et Marie Curie Paris VI)

 Nikolai Nadirashvili (CNRS, Université d'Aix-Marseille)

 Antoine Pauthier (former PhD student, EHESS, Université Paul Sabatier Toulouse III)

 Jean-Michel Roquejoffre (Université Paul Sabatier Toulouse III)

 Lionel Roques (INRA Avignon)

 Luca Rossi (CNRS, EHESS)

 Violaine Roussier-Michon (INSA Toulouse)

 Emmanuel Russ (Université Grenoble Alpes)

 Yannick Sire (on secondment from Université d'Aix-Marseille)




Post-doctoral fellowships


 ANR project NONLOCAL (see abstract) offers post-doctoral fellowships in Paris and/or Toulouse.

 For the applicants: please send a vitae, a covering letter, a list of publications and at least two letters of recommendation (preferably sent by their authors) by mail.




Meetings of the consortium


 January 11-13, 2017, Toulouse

 June 2-3, 2016, Hyères

 November 17-18, 2015, Avignon

 April 16-17, 2015, Paris




Other meetings organized by members of the project and supported by the project


 4th Bath-Paris meeting on branching structures, Paris, June 27-29, 2016

 International Conference on Reaction-Diffusion Equations and Applications to the Life, Social and Physical Sciences, Beijing, May 26-29, 2016

 Nouveaux outils de modélisation pour la biologie, Mont-Serein, November 4-6, 2015

 Conference Recent trends in geometric analysis, Carry-le-Rouet, June 1-5, 2015




Task 1: Propagation phenomena and dynamics of nonlocal equations (scientific lead: Guillemette Chapuisat). Related publications by members of the project:


·      M. Alfaro, J. Coville, G. Raoul, Bistable travelling waves for nonlocal reaction diffusion equations, Disc. Cont. Dyn. Syst. 34 (2014), 1775-1791. (link)

·      M. Alfaro, T. Giletti, Varying the direction of propagation in reaction-diffusion equations in periodic media, Networks Heterog. Media 11 (2016), 369-393. (link)

·      M. Alfaro, T. Giletti, Asymptotic analysis of a monostable equation in periodic media, Tamkang J. Math. 47 (2016), 1-26. (link)

·      H. Berestycki, J. Bouhours, G. Chapuisat, Front blocking and propagation in cylinders with varying cross section, Calc. Var. Part. Diff. Equations 55 (2016), 44. (link)

·      H. Berestycki, A.-C. Coulon, J.-M. Roquejoffre, L. Rossi, The effect of a line with non-local diffusion on Fisher-KPP propagation, Math. Models Methods Appl. Sci. (2015), 2519-2562. (link)

·      H. Berestycki, J.-M. Roquejoffre, L. Rossi, The shape of expansion induced by a line with fast diffusion in Fisher-KPP equations, Comm. Math. Phys. (2016), 207-232. (link)

·      H. Berestycki, J.-M. Roquejoffre, L. Rossi, Travelling waves, spreading and extinction for Fisher-KPP propagation driven by a line with fast diffusion, Nonlinear Anal. 137 (2016), 171-189. (link)

·      O. Bonnefon, J Coville, J. Garnier, L Roques, Inside dynamics of solutions of integro-differential equations, Disc. Cont. Dyn. Syst. B 19 (2014), 3057-3085. (link)

·      J. Bouhours, G. Nadin, A variational approach to reaction diffusion equations with forced speed in dimension 1, Disc. Cont. Dyn. Syst. A 35 (2015), 1843-1872. (link)

·      E. Bouin, V. Calvez, G. Nadin, Hyperbolic traveling waves driven by growth, Math. Models Meth. Appl. Sci. 24 (2014), 1165-1195. (link)

·      E. Bouin, V. Calvez, G. Nadin, Front propagation in a kinetic reaction-transport equation, Arch. Ration. Mech. Anal. 217 (2015), 571-617. (link)

·      Y.-Y. Chen, F. Hamel, J.-S. Guo, Traveling waves for a lattice dynamical system arising in a diffusive endemic model, Nonlinearity, forthcoming. (link)

·      B. Contri, Pulsating fronts for bistable on average reaction-diffusion equations in a time periodic environment, J. Math. Anal. Appl. 437 (2016), 90-132. (link)

·      L. Dietrich, Existence of travelling waves for a reaction–diffusion system with a line of fast diffusion, Appl. Math. Res. Express 2 (2015), 204-252. (link)

·      L. Dietrich, Velocity enhancement of reaction-diffusion fronts by a line of fast diffusion, Trans. Amer. Math. Soc. 369 (2017), 3221-3252. (link)

·      L. Dietrich, J.-M. Roquejoffre, Front propagation directed by a line of fast diffusion: large diffusion and large time asymptotics, J. École Polytechnique 4 (2017), 141-176. (link)

·      W. Ding, F. Hamel, X. Zhao, Transition fronts for periodic bistable reaction-diffusion equations, Calc. Var. Part. Diff. Equations 54 (2015), 2517-2551. (link)

·      W. Ding, F. Hamel, X. Zhao, Bistable pulsating fronts for reaction-diffusion equations in a periodic habitat, Indiana Univ. Math. J., forthcoming. (link)

·      W. Ding, X. Liang, Principal eigenvalues of generalized convolution operators on the circle and spreading speeds of noncompact evolution systems in periodic media, SIAM J. Math. Anal. 47 (2015), 855-896. (link)

·      G. Faye, A. Scheel, Center manifolds without a phase space, Trans. Amer. Math. Soc. (2017), forthcoming. (link)

·      J. Garnier, F. Hamel, L. Roques, Transition fronts and stretching phenomena for a general class of reaction-dispersion equations, Disc. Cont. Dyn. Syst. 37 (2017), 743-756. (link)

·      T. Giletti, F. Hamel, Sharp thresholds between finite spread and uniform convergence for a reaction-diffusion equation with oscillating initial data, J. Diff. Equations 262 (2017), 1461-1498. (link)

·      T. Giletti, L. Monsaingeon, M. Zhou, A KPP road-field system with spatially periodic exchange terms, Nonlinear Anal. TMA 128 (2015), 273-302. (link)

·      L. Girardin, Competition in periodic media: I - Existence of pulsating fronts, Disc. Cont. Dyn. Syst. B (2017), 1341-1360. (link)

·      H. Guo, F. Hamel, Monotonicity of bistable transition fronts in RN, J. Elliptic Parabol. Equations 2 (2016), 145-155. (link)

·      F. Hamel, Bistable transition fronts in RN, Adv. Math. 289 (2016), 279-344. (link)

·      F. Hamel, J. Nolen, J.-M. Roquejoffre, L. Ryzhik, The logarithmic delay of KPP fronts in a periodic medium, J. Europ. Math. Soc. 18 (2016), 465-505. (link)

·      F. Hamel, L. Rossi, Admissible speeds of transition fronts for non-autonomous monostable equations, SIAM J. Math. Anal. 47 (2015), 3342-3392. (link)

·      F. Hamel, L. Rossi, Transition fronts for the Fisher-KPP equation, Trans. Amer. Math. Soc. 368 (2016), 8675-8713. (link)

·      F. Hamel, L. Ryzhik, On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds, Nonlinearity 27 (2014), 2735-2753. (link)

·      Y. Hong, Y. Sire, A new class of traveling solitons for cubic fractional nonlinear Schrödinger equations, Nonlinearity, forthcoming. (link)

·      A. Mellet, J.-M. Roquejoffre, Y. Sire, Existence and asymptotics of fronts in nonlocal combustion models, Comm. Math. Sci. 12 (2014), 1-11. (link)

·      G. Nadin, How does the spreading speed associated with the Fisher-KPP equation depend on random stationary diffusion and reaction terms?  Disc. Cont. Dyn. Syst. B 20 (2015), 1785-1803. (link)

·      G. Nadin, Critical travelling waves for general heterogeneous one-dimensional reaction-diffusion equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), 841-873. (link)

·      G. Nadin, L. Rossi, Transition waves for Fisher-KPP equations with general time-heterogeneous and space-periodic coefficients, Anal. Part. Diff. Equations 8 (2015), 1351-1377. (link)

·      G. Nadin, L. Rossi, Generalized transition fronts for one-dimensional almost periodic Fisher-KPP equations, Arch. Ration. Mech. Anal. (2017), 1239-1267. (link)

·      A. Pauthier, Uniform dynamics for Fisher-KPP propagation driven by a line of fast diffusion under a singular limit, Nonlinearity 28 (2015), 3891-3920. (link)

·      A. Pauthier, The influence of a line with fast diffusion and nonlocal exchange terms on Fisher-KPP propagation, Comm. Math. Sci. 2 (2016), 535-570. (link)

·      L. Rossi, Symmetrization and anti-symmetrization in parabolic equations, Proc. Amer. Math. Soc. (2017), forthcoming. (link)




Task 2: PDEs with integral diffusion, fundamental properties, eigenvalue problems. Links with geometrical equations (scientific lead: Jean-Michel Roquejoffre). Related publications by members of the project:


·      M. Bardi, A. Cesaroni, L. Rossi, Nonexistence of nonconstant solutions of some degenerate Bellman equations and applications to stochastic control, ESAIM Control Optim. Calc. Var. (2016), 842-861. (link)

·      T. Bartsch, L. Jeanjean, Normalized solutions for nonlinear Schrödinger systems, Proc. Royal Soc. Edinburgh A, forthcoming. (link)

·      T. Bartsch, L. Jeanjean, N. Soave, Normalized solutions for a system of coupled cubic Schrödinger equations on R3, J. Math. Pures Appl. 106 (2016), 583-614. (link)

·      J. Bellazzini, N. Boussaid, L. Jeanjean, N. Visciglia, Existence and stability of standing waves for supercritial NLS with a partial confinement, Comm. Math. Phys., forthcoming. (link)

·      J. Bellazzini, L. Jeanjean, On dipolar quantum gases in the unstable regime, SIAM J. Math. Anal. 48 (2016), 2028-2058. (link)

·      H. Berestycki, I. Capuzzo Dolcetta, A. Porretta, L. Rossi, Maximum principle and generalized principal eigenvalue for degenerate elliptic operators, J. Math. Pures Appl. (2015), 1276-1293. (link)

·      M. Bonforte, Y. Sire, J. L. Vazquez, Existence, uniqueness and asymptotic behaviour of fractional porous medium equations in bounded domains, Disc. Cont. Dyn. Syst. 35 (2015), 5725-5767. (link)

·      M. Bonforte, Y. Sire, J.L. Vazquez, Optimal existence and uniqueness theory for the fractional heat equation, Nonlinear Anal., forthcoming. (link)

·      D. Bonheure, F. Hamel, One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in RN, Chinese Ann. Math. Special Issue in Honor of Haïm Brezis 38 B (2017), 149-172. (link)

·      M. Bossy, N. Champagnat, H. Leman, S. Maire, L. Violeau, M. Yvinec, Monte-Carlo methods for linear and non-linear Poisson-Boltzmann equation, ESAIM Proc. Surv. 48 (2015), 420-446. (link)

·      X. Cabré, Y. Sire, Nonlinear equations for fractional laplacians I : regularity, maximum principles and Hamiltonian estimates, Ann. Inst. H. Poincaré, Analyse Non Linéaire 31 (2014), 23-53. (link)

·      X. Cabré, Y. Sire, Nonlinear equations for fractional laplacians II : existence, uniqueness and asymptotics, Trans. Amer. Math. Soc. 367 (2015), 911-941. (link)

·      L. Caffarelli, T. Jin, Y. Sire, J. Xiong, Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities, Arch. Ration. Mech. Anal. 213 (2014), 245-268. (link)

·      F. Campillo, N. Champagnat, C. Fritsch, Links between deterministic and stochastic approaches for invasion in growth-fragmentation-death models, J. Math. Biol. 73 (2016), 1781-1821. (link)

·      F. Campillo, N. Champagnat, C. Fritsch, On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models, Comm. Math. Sci. (2017), forthcoming. (link)

·      D. Castorina, A. Cesaroni, L. Rossi, On a parabolic Hamilton-Jacobi-Bellman equation degenerating at the boundary, Commun. Pure Appl. Anal. (2016), 1251-1263. (link)

·      L. Chen, T. Coulhon, J. Feneuil, E. Russ, Riesz transform for 1≤p≤2 without Gaussian heat kernel bound, J. Geom. Anal., forthcoming. (link)

·      X. Chen, B. Lou, M. Zhou, T. Giletti, Long time behaviour of solutions of a reaction-diffusion equation on unbounded intervals with Robin boundary conditions, Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), 67-92. (link)

·      S. Cingolani, L. Jeanjean K. Tanaka, Multiplicity of positive solutions of nonlinear Schrödinger equation concentrating at a potential well, Calc. Var. Part. Diff. Equations 53 (2015), 413-439. (link)

·      S. Cingolani, L. Jeanjean, K. Tanaka, Multiple complex-valued solutions of nonlinear magnetic Schrödinger equations, J. Fixed Point Theory Appl., forthcoming. (link)

·      J. Coville, F. Li, X. Wang, On eigenvalue problems arising from nonlocal diffusion models, Disc. Cont. Dyn. Syst. 37 (2017), 879-903. (link)

·      J. Davila, L. Lopez, Y. Sire, Bubbling solutions for nonlocal elliptic problems, Rev. Mat. Ibero., forthcoming. (link)

·      Z. Du, C. Gui, Y. Sire, J.-C. Wei, Layered solutions for an inhomogeneous fractional Allen-Cahn equation, Nonlin. Diff. Equations Appl. 23 (2016), 23-29. (link)

·      M. Fazly, Y. Sire, Symmetry results for fractional elliptic systems and related problems, Comm. Part. Diff. Equations 40 (2015), 1070-1095. (link)

·      T. Gou, L. Jeanjean, Existence and orbital statility of standing waves for nonlinear Schrödinger systems, Nonlinear Anal. 144 (2016), 10-22.

·      A. Grigor'yan, N. Nadirasvili, Y. Sire, A lower bound for the number of negative eigenvalues of Schrödinger operators, J. Diff. Geom. 102 (2016), 395-408. (link)

·      F. Hamel, N. Nadirashvili, Shear flows of an ideal fluid and elliptic equations in unbounded domains, Comm. Pure Appl. Math. 70 (2017), 590-608. (link)

·      F. Hamel, N. Nadirashvili, Y. Sire, Convexity of level sets for elliptic problems in convex domains or convex rings: two counterexamples, Amer. J. Math. 138 (2016), 499-527. (link)

·      F. Hamel, X. Ros-Oton, Y. Sire, E. Valdinoci, A one-dimensional symmetry result for a class of nonlocal semilinear equations in the plane, Ann. Inst. H. Poincaré, Analyse Non Linéaire, forthcoming. (link)

·      F. Hamel, E. Russ, Comparison results and improved quantified inequalities for semilinear elliptic equations, Math. Ann. 367 (2017), 311-372. (link)

·      Y. Hong, Y. Sire, On fractional Schrödinger equations in Sobolev spaces, Comm. Pure Appl. Anal. 14 (2015), 2265-2282. (link)

·      L. Jeanjean, T. Luo, Z-Q. Wang, Multiple normalized solutions for quasi-linear Schrödinger equations, J. Diff. Equations 259 (2015), 3894-3928. (link)

·      L. Jeanjean, H. Ramos Quoirin, Multiple solutions for an indefinite elliptic problem with critical growth in the gradient, Proc. Amer. Math. Soc. 144 (2016), 575-586. (link)

·      T. Jin, O. de Queiroz, Y. Sire, J. Xiong, On local behaviour of singular positive solutions to nonlocal elliptic equations, Calc. Var. Part. Diff. Equations 56 (2017). (link)

·      T. Kuusi, G. Mingione, Y. Sire, Nonlocal self-improving properties,  Anal. Part. Diff. Equations 8 (2015), 57-114. (link)

·      T. Kuusi, G. Mingione, Y. Sire, Nonlocal equations with measure data, Comm. Math. Phys. 337 (2015), 1317-1368. (link)

·      J. Leblond, E. Pozzi, E. Russ, Composition operators on generalized Hardy spaces, Compl. Anal. Oper. Theory  9 (2015), 1733-1757. (link)

·      V. Millot, Y. Sire, A fractional Ginzburg-Landau system and half-harmonic maps into spheres, Arch. Ration. Mech. Anal. 215 (2015), 125-210. (link)

·      S. Mirrahimi, J.-M. Roquejoffre, Uniqueness in a class of Hamilton-Jacobi equations with constraints, C. R. Math. Acad. Sci. Paris 353 (2015), 489-494. (link)

·      S. Mirrahimi, J.-M. Roquejoffre, A class of Hamilton-Jacobi equations with constraint: uniqueness and constructive approach, J. Diff. Equations 260 (2016), 4717-4738. (link)

·      P. Mironescu, E. Russ, Traces of weighted Sobolev spaces, Old and new, Nonlinear Anal. TMA 119 (2015), 354-381. (link)

·      N. Nadirashvili, Liouville theorem for Beltrami flow, Geom. Funct. Anal. 24 (2014), 916-921. (link)

·      N. Nadirashvili, Y. Sire, Maximization of higher order eigenvalues and applications, Moscow Math. J. 15 (2015), 767-775. (link)

·      N. Nadirashvili, Y. Sire, Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on S2, J. Diff. Geom., forthcoming. (link)

·      N. Nadirashvili, S. Vladuts, Singular solutions of conformal Hessian equation, Chinese Ann. Math. Special Issue in Honor of Haïm Brezis, forthcoming. (link)

·      M. Novaga, D. Pallara, Y. Sire, A symmetry result for degenerate elliptic equations on the Wiener space with nonlinear boundary conditions and applications, Disc. Cont. Dyn. Syst. S 9 (2016), 815-831. (link)

·      M. Novaga, D. Pallara, Y. Sire, A fractional isoperimetric problem in the Wiener space, J. Anal. Math., forthcoming. (link)

·      G. Palattuci, A. Pisante, Y. Sire, Subcritical approximation of a Yamabe-type non local equation: a G-convergence approach, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XIV (2015), 1-22. (link)

·      A. Petrosyan, W. Shi, Y. Sire, Singular perturbation problem in boundary/fractional combustion, Nonlinear Anal. TMA 138 (2016), 346-368. (link)

·      A. Schikorra, Y. Sire, C. Wang, Weak solutions of geometric flows associated to integro-differential harmonic maps, Manuscripta Math., forthcoming. (link)

·      Y. Sire, J. L. Vazquez, B. Volzone, Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application, Chinese Ann. Math. Special Issue in Honor of Haïm Brezis, forthcoming. (link)

·      J.-C. Wei, Y. Sire, On a fractional Henon equation with applications, Math. Res. Lett. 22 (2015), 1793-1806. (link)




Task 3: Nonlocal equations from mathematical ecology, epidemiology and evolutionary biology (scientific lead: Jérôme Coville). Related publications by members of the project:


·      H. Berestycki, J. Coville, H. H. Vo, Persistence criteria for populations with non-local dispersion, J. Math. Biol. 72 (2016), 1693-1745. (link)

·      H. Berestycki, J. Coville, H. H. Vo, On the definition and the properties of the principal eigenvalue of some non-local operators, J. Funct. Anal. 271 (2016), 2701-2751. (link)

·      O. Bonnefon, J. Coville, G. Legendre, Concentration phenomenon in some non-local equation, Disc. Cont. Dyn. Syst. B 22 (2017), 763-781. (link)

·      A Bonnet, F. Dkhil, E. Logak, Front instability in a condensed phase combustion model, Adv. Nonlinear Anal. 4 (2015), 153-176. (link)

·      C. Carrère, Optimization of an in vitro chemotherapy to avoid resistant tumours, J. Theor. Biol. 413 (2017), 24-33. (link)

·      J. Coville, Nonlocal refuge models with partial control, Disc. Cont. Dyn. Syst. 35 (2015), 1421-1446. (link)

·      J. Fang, G. Faye, Monotone traveling waves for delayed neural field equations, Math. Mod. Meth. Appl. Sci. 26 (2016), 1919-1954. (link)

·      J. Garnier, M. Lewis, Expansion under climate change: the genetic consequences, Bull. Math. Biol. (2016), 2165-2185. (link)

·      M.-E. Gil, F. Hamel, G. Martin and L. Roques, Mathematical properties of a class of integro-differential models from population genetics, SIAM J. Appl. Math., forthcoming. (link)

·      L. Girardin, G. Nadin, Travelling waves for diffusive and strongly competitive systems: relative motility and invasion speed, Europ. J. Appl. Math. 6 (2015), 521-534. (link)

·      E. Logak, I. Passat, An epidemic model with nonlocal diffusion on networks, Netw. Heterog. Media 11 (2016), 693-719. (link)

·      G. Martin, L. Roques, The non-stationary dynamics of fitness distributions: asexual model with epistasis and standing variation, Genetics 204 (2016), 1541-1558. (link)

·      J. Martin, T. Hillen, The spotting distribution of wildfires, Appl. Sci. 6 (2016), 177. (link)

·      L. Roques, O. Bonnefon, Modelling population dynamics in realistic landscapes with linear elements: a mechanistic-statistical reaction-diffusion approach, PLoS ONE 11 (2016), 1-20. (link)

·      L. Roques, E. Walker, P. Franck, S. Soubeyrand, E. Klein, Using genetic data to estimate diffusion rates in heterogeneous landscapes, J. Math. Biol. 73 (2016), 399-422. (link)