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2002 Uniqueness for multi-dimensional Stefan problems with nonlinear boundary conditions described by maximal monotone operators
Toyohiko Aiki
Differential Integral Equations 15(8): 973-1008 (2002).

Abstract

In this paper we discuss weak solutions of the multi-dimensional two-phase Stefan problem with the boundary condition including the subdifferential operator of the convex function on $\mathbb R$ so that the boundary condition is nonlinear and contains a multi-valued operator, in general. Kenmochi and Pawlow already established the uniqueness and existence of a solution to our problem in the sense of the vanishing viscosity solution. The purpose of this paper is to prove the uniqueness theorem for a solution defined in the usual variational sense. Our proof is due to the standard method in which the dual problem of the original problem plays a very important role.

Citation

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Toyohiko Aiki. "Uniqueness for multi-dimensional Stefan problems with nonlinear boundary conditions described by maximal monotone operators." Differential Integral Equations 15 (8) 973 - 1008, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1017.35050
MathSciNet: MR1895575

Subjects:
Primary: 35R35
Secondary: 35K55, 80A22

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 8 • 2002
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