Viscosity Solutions for the two-phase Stefan Problem
Analysis of PDEs
2010-10-21 v1
Abstract
We introduce a notion of viscosity solutions for the two-phase Stefan problem, which incorporates possible existence of a mushy region generated by the initial data. We show that a comparison principle holds between viscosity solutions, and investigate the coincidence of the viscosity solutions and the weak solutions defined via integration by parts. In particular, in the absence of initial mushy region, viscosity solution is the unique weak solution with the same boundary data.
Keywords
Cite
@article{arxiv.1010.4285,
title = {Viscosity Solutions for the two-phase Stefan Problem},
author = {Inwon C. Kim and Norbert Pozar},
journal= {arXiv preprint arXiv:1010.4285},
year = {2010}
}
Comments
28 pages