Ma recherche porte sur l'analyse des EDP, équations intégrales et systèmes intégro-différentiels, et sur l'étude de modèles (déteministes) en maths-bio, écologie, épidémiologie et sciences humaines.
Influence of the geometry on a field-road model : the case of a conical field. Journal of the London Mathematical Society, 2018. Links: Hal, ArXiv.
Propagation properties of reaction-diffusion equations in periodic domains. Analysis and PDE. Links: Hal, ArXiv.
(with L. Rossi) Blocking and invasion for reaction-diffusion equations in periodic media. Calculus of Variations and PDE. Links: Hal, ArXiv.
(with H. Berestycki and L. Rossi) Generalized principal eigenvalues for heterogeneous road-field systems. Communications in Contemporary Mathematics. Links: Hal, ArXiv.
(with H. Berestycki and L. Rossi) Influence of a line with fast diffusion on an ecological niche. Journal of Mathematical Biology. Links: Hal, ArXiv.
Threshold phenomenon and traveling waves for heterogeneous integral equations and epidemic models. Nonlinear Analysis. Links: Hal, ArXiv.
Qualitative properties of spatial epidemiological models. Preprint. Links: Hal, ArXiv.
(With G. Mazanti and F. Santambrogio) Second order local minimal-time Mean Field Games. NoDEA, 2022. Links: Hal, ArXiv.
(With F. Santambrogio and H. Yoldas) A cross-diffusion system obtained via (convex) relaxation in the JKO scheme. Calculus of Variations and PDE, 2023. Links: Hal, ArXiv.
(With M. Alfaro and S. Tréton) The field-road diffusion model: fundamental solution and asymptotic behavior. JDE, 2023. Links : Hal, ArXiv.
(With S. Nordmann) Propagation properties in a multi-species SIR reaction-diffusion system. Journal of Mathematical Biology (2023). Links : Hal, ArXiv.
(With M. Laborde) Long-time behavior of the heterogeneous SIRS epidemiological model. Preprint (2023). Links: Hal, ArXiv.
(With M. Bonnivard, A. Lemenant and A. Zilio) A field-road system with a rectifiable set. Submitted (2024). Links: Hal
(With S. Tréton) Emergence of complexity in opinion propagation: A reaction-diffusion model. Submitted (2024). Links: Hal
Reaction-diffusion equations and systems in heterogeneous media and applications. J'ai soutenu le 25 juin 2018, à l'ENS Paris.
Surface conversion of the dynamics of bacteria escaping chemorepellents (With Lemelle, Braham, Toukabri, Mottin, Fabrege, Calvez, Place). The European Physical Journal E (2024). This is a biology paper, where we describe the spread of E. Coli bacteria using diffusion-convection models. Links: Hal.