15 citations · 27 across the 6 of their papers we have counts for
6 papers · 1 filter
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…
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…
Contraction in and large time behavior for a system arising in chemical reactions and molecular motors
M. Chipot, D. Hilhorst, D. Kinderlehrer +1
We prove a contraction in property for the solutions of a nonlinear reaction--diffusion system whose special cases include intercellular transport as well as reversible chemi…
Long time convergence for a class of variational phase field models
Pierluigi Colli, Danielle Hilhorst, Francoise Issard-Roch +1
In this paper we analyze a class of phase field models for the dynamics of phase transitions which extend the well-known Caginalp and Penrose-Fife models. Existence and uniqueness…
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…
On long-time dynamics for competition-diffusion systems with inhomogeneous Dirichlet boundary conditions
E. C. M. Crooks, E. N. Dancer, D. Hilhorst
We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition param…