79 citations · 141 across the 22 of their papers we have counts for
25 papers
The vanishing latent heat limit of a stochastic Stefan problem : An error estimate
Ioana Ciotir, Perla El Kettani, Dan Goreac +1
The purpose of this paper is to extend an article by Hilhorst, Mimura and Sch{ä}tzle [18] about the limit as the latent heat coefficient tends to zero of a two-phase Stefan problem…
Convergence of solutions of a one-phase Stefan problem with Neumann boundary data to a self-similar profile
Danielle Hilhorst, Sabrina Roscani, Piotr Rybka
We study a one-dimensional one-phase Stefan problem with a Neumann boundary condition on the fixed part of the boundary. We construct the unique self-similar solution, and show tha…
Fick's las selects the Neumann boundary condition
Danielle Hilhorst, Seung-Min Kang, Ho-Youn Kim +1
We study the appearance of a boundary condition along an interface between two regions, one with constant diffusivity and the other with diffusivity $\eps>0$, when $\eps\to0$.…
Singular limit of an Allen-Cahn equation with nonlinear diffusion
Perla El Kettani, Tadahisa Funaki, Danielle Hilhorst +2
We consider an Allen-Cahn equation with nonlinear diffusion, motivated by the study of the scaling limit of certain interacting particle systems. We investigate its singular limit…
A hyperbolic-elliptic-parabolic PDE model describing chemotactic E. coli colonies
Danielle Hilhorst, Pierre Roux
We study a modified version of an initial-boundary value problem describing the formation of colony patterns of bacteria \textit{Escherichia Coli}. The original system of three par…
Spatial segregation limit of traveling wave solutions for a fully nonlinear strongly coupled competitive system
Léo Girardin, Danielle Hilhorst
The paper is concerned with a singular limit for the bistable traveling wave problem in a very large class of two-species fully nonlinear parabolic systems with competitive reactio…