# American Institute of Mathematical Sciences

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

## On instant extinction for very fast diffusion equations

 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.
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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