Research

My research focuses on the analysis of PDE, integral equations and integro-differential systems, and on the study of (deterministic) models from biology, ecology and epidemiology.

Publications et preprints

1. 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.

2. Propagation properties of reaction-diffusion equations in periodic domains. Analysis and PDE. Links: Hal, ArXiv.

3. (with L. Rossi) Blocking and invasion for reaction-diffusion equations in periodic media. Calculus of Variations and PDE. Links: Hal, ArXiv.

4. (with H. Berestycki and L. Rossi) Generalized principal eigenvalues for heterogeneous road-field systems. Communications in Contemporary Mathematics. Links: Hal, ArXiv.

5. (with H. Berestycki and L. Rossi) Influence of a line with fast diffusion on an ecological niche. Journal of Mathematical Biology. Links: Hal, ArXiv.

6. Threshold phenomenon and traveling waves for heterogeneous integral equations and epidemic models. Nonlinear Analysis. Links: Hal, ArXiv.

7. Qualitative properties of spatial epidemiological models. Preprint. Links: Hal, ArXiv.

8. (With G. Mazanti and F. Santambrogio) Second order local minimal-time Mean Field Games. NoDEA, 2022. Links: Hal, ArXiv.

9. (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.

10. (With M. Alfaro and S. Tréton) The field-road diffusion model: fundamental solution and asymptotic behavior. JDE, 2023. Links : Hal, ArXiv.

11. (With S. Nordmann) Propagation properties in a multi-species SIR reaction-diffusion system. Journal of Mathematical Biology (2023). Links : Hal, ArXiv.

12. (With M. Laborde) Long-time behavior of the heterogeneous SIRS epidemiological model. Preprint (2023). Links: Hal, ArXiv.

PhD Manuscript

Reaction-diffusion equations and systems in heterogeneous media and applications.  Defended  in 2018, june, 25th at l'ENS Paris.

Other

Surface conversion of escape wave dynamics of chemotactic bacteria (With Lemelle, Braham, Toukabri, Mottin, Fabrege, Calvez, Place). Preprint. This is a biology paper, where we describe the spread of E. Coli bacteria using diffusion-convection models.