8 citations · 8 across the 4 of their papers we have counts for
4 papers
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…
The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system
Matthieu Alfaro, Danielle Hilhorst, Hiroshi Matano
We consider an Allen-Cahn type equation with a bistable nonlinearity associated to a double-well potential whose well-depths can be slightly unbalanced, and where the coefficient o…