40 citations · 264 across the 35 of their papers we have counts for
4 papers · 2 filters
Generation of interface for an Allen-Cahn equation with nonlinear diffusion
Matthieu Alfaro, Danielle Hilhorst
In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behav…
The Singular Limit of a Chemotaxis-Growth System with General Initial Data
Matthieu Alfaro
We study the singular limit of a system of partial differential equations which is a model for an aggregation of amoebae subjected to three effects: diffusion, growth and chemotaxi…
Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation
Matthieu Alfaro, Harald Garcke, Danielle Hilhorst +2
We study the singular limit of a spatially inhomogeneous and anisotropic reaction-diffusion equation. We use a Finsler metric related to the anisotropic diffusion term and work in…
Generation, motion and thickness of transition layers for a nonlocal Allen-Cahn equation
Matthieu Alfaro
We investigate the behavior, as a small parameter tends to zero, of a nonlocal Allen-Cahn equation. Given a rather general initial data, we perform a rigorous analysis of both the…