Viscosity Solutions for the two-phase Stefan Problem

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.

28 pages

Cited by in corpus (1)

• Two phase Stefan-type problem: Regularization near initial data by phase dynamics