Electron. J. Diff. Eqns., Vol. 2005(2005), No. 23, pp. 1-7.

Extinction for fast diffusion equations with nonlinear sources

Yuxiang Li, Jichun Wu

Abstract:
We establish conditions for the extinction of solutions, in finite time, of the fast diffusion problem
$u_t=\Delta u^m+\lambda u^p$,
0 less than $m$ less than 1, in a bounded domain of $R^N$ with N greater than 2. More precisely, we show that if p greater than m, the solution with small initial data vanishes in finite time, and if p less than m, the maximal solution is positive for all t greater than 0. If $p=m$, then first eigenvalue of the Dirichlet problem plays a role.

Submitted September 15, 2004. Published February 20, 2005.
Math Subject Classifications: 35K20, 35K55.
Key Words: Extinction; fast diffusion; first eigenvalue.

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Yuxiang Li
Department of Mathematics, Southeast University
Nanjing 210096, China.
Department of Earth Sciences, Nanjing University
Nanjing 210093, China
email: lieyuxiang@yahoo.com.cn
  Jichun Wu
Department of Earth Sciences, Nanjing University
Nanjing 210093, China
email: jcwu@nju.edu.cn

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