Viscosity Solutions for the two-phase Stefan Problem

2010/10/20 by Inwon C. Kim, Kim, Inwon C., Norbert Požár +1
Computer Science · Mathematics · #35R35 80A22 35B51 35D40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1010.4285

openalex publication_date 2010/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Similarity solution for a two-phase one-dimensional Stefan problem with\n a convective boundary condition and a mushy zone model