40 citations · 264 across the 35 of their papers we have counts for
4 papers · 2 filters
Generation of fine transition layers and their dynamics for the stochastic Allen--Cahn equation
Matthieu Alfaro, Dimitra Antonopoulou, Georgia Karali +1
We study an $\ep$-dependent stochastic Allen--Cahn equation with a mild random noise on a bounded domain in , . Here $\ep$ is a small positive parameter that…
When fast diffusion and reactive growth both induce accelerating invasions
Matthieu Alfaro, Thomas Giletti
We focus on the spreading properties of solutions of monostable equations with fast diffusion. The nonlinear reaction term involves a weak Allee effect, which tends to slow down th…
Evolutionary branching via replicator-mutator equations
Matthieu Alfaro, Mario Veruete
We consider a class of non-local reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. For a confining fitness function, we prove well-…
Population invasion with bistable dynamics and adaptive evolution: the evolutionary rescue
Matthieu Alfaro, Arnaud Ducrot
We consider the system of reaction-diffusion equations proposed in [8] as a population dynamics model. The first equation stands for the population density and models the ecologica…