On instant extinction for very fast diffusion equations

Yun-Gang Chen; Yoshikazu Giga; Koh Sato

doi:10.3934/dcds.1997.3.243

Article Contents

1997, Volume 3, Issue 2: 243-250. Doi: 10.3934/dcds.1997.3.243

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On instant extinction for very fast diffusion equations

1.
Hokkaido Tokai University, Sapporo 005
2.
Department of Mathematics, Hokkaido University, Sapporo 060
3.
Department of Social Science and Information, Otaru University of Commerce, Otaru 047

Received: September 30, 1996

Revised: December 31, 1996

Published: March 1997

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Abstract

In this paper we prove instant extinction of the solutions to Dirichlet and Neumann boundary value problem for some quasilinear parabolic equations whose diffusion coefficient is singular when the spatial gradient of unknown function is zero.

Keywords:

Dirichlet and Neumann boundary value problem,
quasilinear parabolic equations.

Mathematics Subject Classification: 35K55, 35B40.

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