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April  1997, 3(2): 243-250. doi: 10.3934/dcds.1997.3.243

On instant extinction for very fast diffusion equations

Yun-Gang Chen 1, , Yoshikazu Giga 2, and  Koh Sato 3,

1. 

Hokkaido Tokai University, Sapporo 005, Japan
2. 

Department of Mathematics, Hokkaido University, Sapporo 060
3. 

Department of Social Science and Information, Otaru University of Commerce, Otaru 047, Japan

Received  October 1996 Revised  January 1997 Published  January 1997

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, 35B4.
Citation: Yun-Gang Chen, Yoshikazu Giga, Koh Sato. On instant extinction for very fast diffusion equations. Discrete & Continuous Dynamical Systems, 1997, 3 (2) : 243-250. doi: 10.3934/dcds.1997.3.243
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