Extinction for fast diffusion equations with nonlinear sources
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2005-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2005/23/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |