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1995 Global behaviour of solutions to a parabolic mean curvature equation
Bernd Kawohl, Nickolai Kutev
Differential Integral Equations 8(8): 1923-1946 (1995).

Abstract

Consider (1.1) for a domain $\Omega$ for which there is no classical nonparametric solution of the stationary problem. We study viscosity solutions of (1.1). In general they fail to satisfy Dirichlet data on the boundary and "detach." In fact the solution tends to infinity with finite speed. The velocity stabilizes as $t\to \infty$, and we give some results on asymptotic growth. These new effects can be reconciled with the notion of viscosity solutions. The free boundary data are shown to be Lipschitzian for special domains $\Omega$. Problem (1.1) is related to some isoperimetric geometric problem.

Citation

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Bernd Kawohl. Nickolai Kutev. "Global behaviour of solutions to a parabolic mean curvature equation." Differential Integral Equations 8 (8) 1923 - 1946, 1995.

Information

Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0844.35050
MathSciNet: MR1348958

Subjects:
Primary: 35K60
Secondary: 35B40, 35D99, 53A10

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 8 • 1995
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