Reaction-diffusion : basic papers
- A.N. KOLMOGOROV, I.G. PETROVSKII, N.S. PISKUNOV, "Etude de l’équation de diffusion avec accroissement de la quantité de matière, et son application à un problème biologique", Bjul. Moskowskogo Gos. Univ., 17 (1937), 1–26.
- D.G. ARONSON, H.F. WEINBERGER, "Multidimensional nonlinear diffusion arising in population genetics", Advances in Mathematics, 30, 1 (1976), 33-76.
- H. BERESTYCKI, F. HAMEL, "Generalized transition waves and their properties", Communications on Pure and Applied Mathematics, 65, 5 (2012), 592-648, arXiv:1012.0794.
Program 1. Propagation in heterogeneous media. Related questions for PDEs with integral diffusion.
Sub-program: Spreading speeds.
Generalized eigenvalues
- H. BERESTYCKI, L. ROSSI, "Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains", Communication on Pure and Applied Mathematics, 68, 6 (2015), 1014-1065, arXiv:1008.4871.
- H. BERESTYCKI, I. CAPUZZO DOLCETTA, A. PORRETTA, L. ROSSI, "Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators", Journal de Mathématiques Pures Appliquées, 103, 5 (2015), 1276-1293, preprint.
- P.-T. NGUYEN, H.-H. VO, "Existence, uniqueness and qualitative properties of positive solutions of quasilinear elliptic equations", Journal of Functional Analysis, 269, 10 (2015), 3120-3146, arXiv:1407.6931.
- H. BERESTYCKI, J. COVILLE, H.-H. VO, "On the definition and the properties of the principal eigenvalue of some nonlocal operators", Journal of Functional Analysis, 271, 10 (2016), 2701-2751, arXiv:1512.06529.
Spreading in heterogeneous media
- F. HAMEL, A. ZLATOS, "Speed-up of combustion fronts in shear flows", Mathematische Annalen, 356, 3 (2013), 845-867, arXiv:1112.3199.
- H. BERESTYCKI, G. NADIN, "Spreading speeds for one-dimensional monostable reaction-diffusion", Journal of Mathematical Physics, 53, 11 (2012), preprint.
- G. NADIN, "How does the spreading speed associated with the Fisher-KPP equation depend on random stationary diffusion and reaction terms ?", Discrete and Continuous Dynamical Systems - Series B, 20, 6 (2015), 1785-1803, arXiv:1609.01441.
- L. ROSSI, "The Freidlin-Gärtner formula for general reaction terms", preprint (2015), arXiv:1503.09010.
- J. FANG, X. YU, X.-Q. ZHAO, "Traveling waves and spreading speeds for time-space periodic monotone systems", submitted (2015), arXiv:1504.03788.
- H. BERESTYCKI, G. NADIN, "Asymptotic spreading for general heterogeneous Fisher-KPP type equations", (2017), preprint.
- R. DUCASSE, "Propagation properties of reaction-diffusion equations in periodic domains", submitted (2017), arXiv:1709.07197.
Propagation in nonlocal equations
- X. CABRE, A.-C. COULON, J.-M. ROQUEJOFFRE, "Propagation in Fisher-KPP type equations with fractional diffusion in periodic media", Compte-rendus de l'Académie des Sciences - Mathématique, 350, 19-20 (2012), 885-890, preprint.
- A.-C. COULON, M. YANGARI, "Exponential propagation for fractional reaction-diffusion cooperative systems with fast decaying initial conditions", Journal of Dynamics and Differential Equations, 27 (2015), 1-17, arXiv:1405.5113.
- E. BOUIN, V. CALVEZ, G. NADIN, "Propagation in a kinetic reaction-transport equation: travelling waves and accelerating fronts", Archive for Rational Mechanics and Analysis, 217, 2 (2015), 571-617, preprint.
- J. GARNIER, F. HAMEL, L. ROQUES, "Transition fronts and stretching phenomena for a general class of reaction-dispersion equations", Discrete and Continuous Dynamical Systems - Series A, 37, 2 (2017), 743-756, preprint.
- H. BERESTYCKI, T. JIN, L. SILVESTRE, "Propagation in a non local reaction diffusion equation with spatial and genetic trait structure", Nonlinearity, 29, 4 (2016), 1434-1466, arXiv:1411.2019.
- J.-M. ROQUEJOFFRE, A. TARFULEA, "Gradient estimates and symmetrization for the Fisher-KPP equation with fractional diffusion", submitted, arXiv:1502.06304.
- H. BERESTYCKI, N. RODRIGUEZ, "A non-local bistable reaction-diffusion equation with a gap", Discrete and Continuous Dynamical Systems - Series A, 37, 2 (2017), 685-723.
Time delays in Fisher-KPP equations
- J. NOLEN, J.-M. ROQUEJOFFRE, L. RYZHIK, "Power-like delay in time inhomogeneous Fisher-KPP equations", Communications in Partial Differential Equations, 40, 3 (2015), 475-505, preprint.
- F. HAMEL, J. NOLEN, J.-M. ROQUEJOFFRE, L. RYZHIK, "The logarithmic delay of KPP fronts in a periodic medium", Journal of the European Mathematical Society, 18, 2 (2016), 465-505, arXiv:1211.6173.
Sub-program: Theory of transition fronts.
Steady states: existence, stability, persistence
- H. BERESTYCKI, J. COVILLE, H.H. VO, "Persistence criteria for populations with non-local dispersion", Journal of Mathematical Biology, 72, 7 (2016), 1-53, 1693-1745, arXiv: 1406.6346.
- H. BERESTYCKI, T.-C. LIN, J. WEI, C. ZHAO, "On Phase-Separation Model : Asymptotics and Qualitative Properties", Archive for Rational Mechanics and Analysis, 208, 1 (2013), 163-200, preprint.
- H.-H. VO, "Persistence versus extinction under a climate change in mixed environments", Journal of Differential Equations, 259, 10 (2015), 4947-4988, arXiv:1412.0907.
- H. BERESTYCKI, A. ZILIO, "Predators-prey models with competition: the emergence of territoriality", (2017), submitted, preprint.
- H. BERESTYCKI, A. ZILIO, "Predators-prey models with competition, Part I : existence, bifurcation and qualitative properties", (2017), preprint.
- S. TERRACINI, G. VERZINI, A. ZILIO, "Spiraling asymptotic profiles of competition-diffusion systems" (2017), preprint.
Forced speed and delays in reaction-diffusion equations. Related questions of climate change modelling
- H. BERESTYCKI, L. DESVILLETTES, O. DIEKMANN, "Can climate change lead to gap formation ?", Ecological complexity, 20 (2014), 264-270.
- A. DUCROT, G. NADIN, "Asymptotic behaviour of travelling waves for the delayed Fisher-KPP equation", Journal of Differential Equations, 256, 9 (2014), 3115–3140, preprint.
- J. BOUHOURS, G. NADIN, "A variational approach to reaction diffusion equations with forced speed in dimension 1", Discrete and Continuous Dynamical Systems A, 35, 5 (2015), 1843–1872, arXiv:1310.3689.
- M. ALFARO, H. BERESTYCKI, G. RAOUL, "The effect of climate shift on a species submitted to dispersion, evolution, growth and nonlocal competition", SIAM Journal on Mathematical Analysis, 49, 1 (2017), 562-596, arXiv:1511.05110.
Travelling and pulsating fronts: inside structure, dynamics
- H. BONNEFON, J. COVILLE, J. GARNIER, F. HAMEL, L. ROQUES, "The spatio-temporal dynamics of neutral genetic diversity", Ecological Complexity, 20 (2014), 282-292, preprint.
- L. ROQUES, Y. HOSONO, O. BONNEFON, T. BOIVIN, "The effect of competition on the neutral intraspecific diversity of invasive species", Journal of Mathematical Biology, 71, 2 (2015), 465-489.
- L. GIRARDIN, G. NADIN, "Travelling waves for diffusive and strongly competitve systems: relative motility and invasion speed", European Journal of Applied Mathematics, 26, 4 (2015), 521-534, arXiv:1503.06076.
- B. CONTRI, "Pulsating fronts for bistable on average reaction-diffusion equations in a time periodic environment", Journal of Mathematical Analysis and Applications, 437, 1 (2016), 90-132, arXiv:1507.06060.
Transition fronts in homogeneous or heterogeneous media
- F. HAMEL, L. ROSSI, "Transition fronts for the Fisher-KPP equation", Transactions of the American Mathematical Society, 368, 12 (2016), 8675-8713, arXiv:1404.2821.
- F. HAMEL, "Bistable transition fronts in Rn", Advances in Mathematics, 289 (2016), 279-344, arXiv:1302.4817.
- W. DING, F. HAMEL, X. ZHAO, "Transition fronts for periodic bistable reaction-diffusion equations", Calculus of Variations and Partial Differential Equations, 54, 3 (2015), 2517-2551, preprint.
- F. HAMEL, L. ROSSI, "Admissible speeds of transition fronts for non-autonomous monostable equations", SIAM Journal on Mathematical Analysis, 47, 5 (2015), 3342-3392, preprint.
- G. NADIN, L. ROSSI, "Transition waves for Fisher-KPP equations with general time-heterogeneous and space-periodic coefficients", Analysis and PDE, 8, 6 (2015), 1351-1377, preprint.
Sub-program: KPP type models with long range spatial competition
- F. HAMEL, L. RYZHIK, "On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds", Nonlinearity, 27, 11 (2014), 2735, arXiv:1307.3001.
- G. FAYE, M. HOLZER, "Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical system approach", Journal of Differential Equations, 258, 7 (2015), 2257-2289, preprint.
- S. MIRRAHIMI, J.-M. ROQUEJOFFRE, "Uniqueness in a class of Hamilton-Jacobi with constraints", Comptes Rendus Mathématique de l'Académie des Sciences de Paris, 353, 6 (2015), 489-494, arXiv:1502.04002.
- S. MIRRAHIMI, J.-M. ROQUEJOFFRE, "A class of Hamilton-Jacobi equations with constraints: uniqueness and constructive approach", Journal of Differential Equations, 260, 5 (2016), 4717-4738, arXiv:1505.05994.
- N. SOAVE, H. TAVARES, S. TERRACINI, A. ZILIO, "Variational problems with long-range interaction", submitted (2017), arXiv:1707.05005.
Sub-program: Links with geometrical equations.
Program 2. Analysis of models from mathematical economy, ecology, medicine and social sciences.
Sub-program: Interaction between integral and local diffusion in invasion models.
The influence of a line of fast diffusion on reaction-diffusion propagation
Interaction of spatial scales in complex systems
Sub-program: Non-local free boundary problems arising in modeling the role of heterogeneities in the formation of asset prices bubbles.
1. H. BERESTYCKI, R. MONNEAU, J.A. SCHEINKMAN, "A non local free boundary problem arising in a theory of financial bubbles", Philosophical Transactions of the Royal Society A, 372, 2028 (2014), preprint.
2. H. BERESTYCKI, C. BRUGGEMAN, R. MONNEAU, J.A. SCHEINKMAN, "Bubbles in assets with finite life", (2016), submitted, preprint.
Sub-program: An application in medicine: propagation of a migraine with aura.
- H. BERESTYCKI, S. TERRRACINI, K. WANG, J-C. WEI, "On Entire Solutions of an Elliptic System Modeling Phase Separations", Advances in Mathematics, 243 (2013), 102-126, arXiv:1204.1038.
- F. HAMEL, N. NADIRASHVILI, Y. SIRE, "Convexity of level sets for elliptic problems in convex domains or convex rings: two counterexamples", American Journal of Mathematics, 138, 2 (2016), 499-527, preprint.
- A. ZILIO, "Optimal regularity results related to a partition problem involving the half-Laplacian", International Series of Numerical Mathematics, 166 - New Trends in Shape Optimization (2015), 301-314, preprint.
- N. SOAVE, A . ZILIO, "On phase separation in systems of coupled elliptic equations: asymptotic analysis and geometric aspects", Annales de l'Institut Henri Poincare (C) Non Linear Analysis, in press (2016), preprint.
- N. SOAVE, H. TAVARES, S. TERRACINI, A. ZILIO, "Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations with nontrivial grouping", Nonlinear Analysis, 138 (2016), 388-427, preprint.
- N. SOAVE, A . ZILIO, "Multidimensional entire solutions for an elliptic system modelling phase separation", Analysis and PDE, 9, 5 (2016), 1019-1041, preprint.
Program 2. Analysis of models from mathematical economy, ecology, medicine and social sciences.
Sub-program: Interaction between integral and local diffusion in invasion models.
The influence of a line of fast diffusion on reaction-diffusion propagation
- H. BERESTYCKI, J.-M. ROQUEJOFFRE, L. ROSSI, "The influence of a line with fast diffusion on Fisher-KPP propagation", Journal of Mathematical Biology, 66, 4 (2013), 743-766, arXiv:1210.3721.
- H. BERESTYCKI, J.-M. ROQUEJOFFRE, L. ROSSI, "Fisher-KPP propagation in the presence of a line: further effects", Nonlinearity, 26, 9 (2013), 2623-2640, arXiv:1303.1091.
- H. BERESTYCKI, J.-M. ROQUEJOFFRE, L. ROSSI, "The shape of expansion induced by a line with fast diffusion in Fisher-KPP equations", Communication in Mathematical Physics, 343, 1 (2016), 207-232, arXiv:1402.1441.
- H. BERESTYCKI, A.-C. COULON, J.-M. ROQUEJOFFRE, L. ROSSI, "Speed-up of reaction-diffusion fronts by a line of fast diffusion", Séminaire Laurent Schwartz - EDP et applications, 25, 13 (2013-2014), 1-25.
- H. BERESTYCKI, A.-C. COULON, J.-M. ROQUEJOFFRE, L. ROSSI, "The effect of a line of nonlocal diffusion on Fisher-KPP propagation", Mathematical Models and Methods in Applied Sciences, 25, 13 (2015), 2519-2562, preprint.
- L. DIETRICH, "Existence of travelling waves for a reaction-diffusion system with a line of fast diffusion", Applied Mathematics Research Express, 2 (2015), 204-252, arXiv:1410.4736.
- L. DIETRICH, "Velocity enhancement of reaction-diffusion fronts by a line of fast diffusion", Transactions of the American Mathematical Society, 369 (2017), 3221-3252, arXiv:1410.4738.
- A. PAUTHIER, "The influence of a line with fast diffusion and nonlocal exchange terms on Fisher-KPP propagation", Communication in Mathematical Sciences, 14, 2 (2016), 535-570, arXiv:1410.1584.
- A. PAUTHIER, "Uniform dynamics for Fisher-KPP propagation driven by a line of fast diffusion under a singular limit", Nonlinearity, 28, 11 (2015), arXiv:1411.2426.
- A. PAUTHIER, "Road-field reaction-diffusion system: a new threshold for long range exchanges", preprint (2015), arXiv:1504.05437.
- A. TELLINI, "Propagation speed in a strip bounded by a line with different diffusion", Journal of Differential Equations, 260, 7 (2016), 5956–5986, preprint.
- L. ROSSI, A. TELLINI, E. VALDINOCI, "The effect on Fisher-KPP propagation in a cylinder with fast diffusion on the boundary", submitted (2017), preprint.
- R. DUCASSE, "Influence of the geometry on a field-road model : the case of a conical field", preprint (2017), arXiv:1705.01304.
- H. BERESTYCKI, N. RODRIGUEZ, L. RYZHIK, "Traveling Wave Solutions in a Reaction-Diffusion Model for Criminal Activity", SIAM Multiscale Modeling and Simulation, 11, 4 (2013), 1097-1126, arXiv:1302.4333.
- H. BERESTYCKI, J.-C. WEI, M. WINTER, "Existence of symmetric and asymmetric spikes for a crime hotspot model", SIAM Journal on Mathematical Analysis, 46, 1 (2014),691-719, arXiv:1311.2086.
- H. BERESTYCKI, J.-P. NADAL, N. RODRIGUEZ, "A model of riots dynamics: shocks, diffusions and thresholds", Networks and Heterogeneous Media, 10, 3 (2015), 443-475, arXiv:1502.04725.
- H. BERESTYCKI, N. RODRIGUEZ, "Analysis of a heterogeneous model for riot dynamics : the effect of censorship of information", European Journal of Applied Mathematics, 27, 3 (2016), 554-582, arXiv:1502.04735.
- L. BONNASSE-GAHOT, H. BERESTYCKI, M.-A. DEPUISET, M. GORDON, J.-P. NADAL, S. ROCH, N. RODRIGUEZ, "Epidemiological modeling of the 2005 French riots : a spreading wave and the role of contagion", (2017), Scientific Reports, to appear in 2018, arXiv:1707.07479.
- H. BERESTYCKI, N. RODRIGUEZ, L. ROSSI, "Periodic cycles of rioting activity", Journal of Differential Equations (2018), to appear, preprint, DOI: 10.1016/j.jde.2017.09.005.
Interaction of spatial scales in complex systems
- M. BARTHELEMY, P. BORDIN, H. BERESTYCKI, M. GRIBAUDI, "Self-organization versus top-down planning in the evolution of a city", Scientific Reports, 3 ,2153 (2013), arXiv:1307.2203.
- L. ROQUES, J.-P. ROSSI, H. BERESTYCKI, J. ROUSSELET, J. GARNIER, J.-M. ROQUEJOFFRE, L. ROSSI, S. SOUBEYRABD, C. ROBINET, "Modeling the spatio-temporal dynamics of the pine processionary moth", in Processionary Moths and Climate Change: An Update, Springer (2014), 227-263.
Sub-program: Non-local free boundary problems arising in modeling the role of heterogeneities in the formation of asset prices bubbles.
1. H. BERESTYCKI, R. MONNEAU, J.A. SCHEINKMAN, "A non local free boundary problem arising in a theory of financial bubbles", Philosophical Transactions of the Royal Society A, 372, 2028 (2014), preprint.
2. H. BERESTYCKI, C. BRUGGEMAN, R. MONNEAU, J.A. SCHEINKMAN, "Bubbles in assets with finite life", (2016), submitted, preprint.
Sub-program: An application in medicine: propagation of a migraine with aura.
- H. BERESTYCKI, G. CHAPUISAT, "Traveling fronts guided by the environment for reaction-diffusion equations", Networks and Heterogeneous Media, 8, 1 (2013), 79-114, arXiv:1206.6575.
- H. BERESTYCKI, J. BOUHOURS, G. CHAPUISAT, "Front blocking and propagation in cylinders with varying cross-section", Calculus of Variations and Partial Differential Equations, 55, 3 (2016), 1-32, arXiv:1501.01326.