40 citations · 264 across the 35 of their papers we have counts for
41 papers
Propagation or extinction in bistable equations: the non-monotone role of initial fragmentation
Matthieu Alfaro, François Hamel, Lionel Roques
In this paper, we investigate the large-time behavior of bounded solutions of the Cauchy problem for a reaction-diffusion equation in with bistable reaction term. We…
The field-road diffusion model: fundamental solution and asymptotic behavior
Matthieu Alfaro, Romain Ducasse, Samuel Tréton
We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. This system takes the form of a system of PDEs set on domains of d…
Quantifying the threshold phenomena for propagation in nonlocal diffusion equations
Matthieu Alfaro, Arnaud Ducrot, Hao Kang
We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the so-called bistable and ignition case…
Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics
Matthieu Alfaro, Pierre Gabriel, Otared Kavian
We consider nonlinear mutation selection models, known as replicator-mutator equations in evolutionary biology. They involve a nonlocal mutation kernel and a confining fitness pote…
Lotka-Volterra competition-diffusion system: the critical competition case
Matthieu Alfaro, Dongyuan Xiao
We consider the reaction-diffusion competition system in the so-called {\it critical competition case}. The associated ODE system then admits infinitely many equilibria, which make…
On the modelling of spatially heterogeneous nonlocal diffusion: deciding factors and preferential position of individuals
Matthieu Alfaro, Thomas Giletti, Yong-Jung Kim +2
We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the…