3 papers
math.AP2026
Thresholds, fragmentation and symmetrization in parabolic equations
Matthieu Alfaro, Yihong Du, François Hamel +1
This paper is mainly concerned with the large-time dynamics of bounded nonnegative solutions of reaction-diffusion equations on the real line with nonlinearities mainly of the bist…
math.AP2025
Existence of two thresholds in a bistable equation with nonlocal competition
Matthieu Alfaro, Cédric Chane Ki Chune, Lionel Roques
We consider a nonlocal bistable reaction-diffusion equation, which serves as a model for a population structured by a phenotypic trait, subject to mutation, trait-dependent fitness…
math.AP2024
A host-pathogen coevolution model. Part I: Run straight for your life
Matthieu Alfaro, Florian Lavigne, Lionel Roques
In this study, we propose a novel model describing the coevolution between hosts and pathogens, based on a non-local partial differential equation formalism for populations structu…