A generalized one phase Stefan problem as a vanishing viscosity limit
Analysis of PDEs
2020-08-11 v2
Abstract
We study the vanishing viscosity limit of a nonlinear diffusion equation describing chemical reaction interface or the spatial segregation interface of competing species, where the diffusion rate for the negative part of the solution converges to zero. As in the standard one phase Stefan problem, we prove that the positive part of the solution converges uniformly to the solution of a generalized one phase Stefan problem. This information is then employed to determine the limiting equation for the negative part, which is an ordinary differential equation.
Keywords
Cite
@article{arxiv.2004.06460,
title = {A generalized one phase Stefan problem as a vanishing viscosity limit},
author = {Kelei Wang},
journal= {arXiv preprint arXiv:2004.06460},
year = {2020}
}
Comments
18 pages, title changed, accepted for publication in Portugaliae Mathematica