79 citations · 141 across the 22 of their papers we have counts for
4 papers · 1 filter
Singular limit of a two-phase flow problem in porous medium as the air viscosity tends to zero
Robert Eymard, Marie Henry, Danielle Hilhorst
In this paper we consider a two-phase flow problem in porous media and study its singular limit as the viscosity of the air tends to zero; more precisely, we prove the convergence…
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…
Mass conserved Allen-Cahn equation and volume preserving mean curvature flow
Xinfu Chen, Danielle Hilhorst, Elisabeth Logak
We consider a mass conserved Allen-Cahn equation $u_t=Δu+ \e^{-2} (f(u)-\eλ(t))$ in a bounded domain with no flux boundary condition, where $\eλ(t)$ is the average of $f(u(\cdot,t)…