Viscosity Solutions for the two-phase Stefan Problem

Details Viscosity Solutions for the two-phase Stefan Problem Viscosity Solutions for the two-phase Stefan Problem

2010-10-20

arxiv.org/abs/1010.4285v1

Mathematics

Analysis of PDEs

28 pages

Scientific paper

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.

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