Inwon C. Kim, Norbert Pozar
Published 2010-10-20Version 1
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.
Boundary controllability of phase-transition region of a two-phase Stefan problem
Viscosity solutions of contact Hamilton-Jacobi equations without monotonicity assumptions
Uniqueness for solutions of the two-phase Stefan problem with signed measures as data
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