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| Increasing Powers in a Degenerate Parabolic Logistic Equation |
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Citation： |
Jos´e Francisco RODRIGUES,Hugo TAVARES.Increasing Powers in a Degenerate Parabolic Logistic Equation[J].Chinese Annals of Mathematics B,2013,34(2):277~284 |
| Page view： 2416
Net amount： 2402 |
Authors： |
Jos′e Francisco RODRIGUES; Hugo TAVARES; |
Foundation： |
Funda\c c\~ao para a Ci\^encia e a Tecnologia (FCT) (No. PEst OE/MAT/UI0209/ 2011). The second author was also supported by an FCT grant (No. SFRH/BPD/69314/201). |
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| Abstract： |
The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem $$ \partial_t u-\Delta u=a u-b(x) u^p \quad \text{ in } \Omega\times \R^+,\quad u(0)=u_0,\quad u(t)|_{\partial\Omega}=0,$$ as $p\to +\infty$, where $\Omega$ is a bounded domain, and $b(x)$ is a nonnegative function. The authors deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards fully describe its long time behavior. |
Keywords： |
Parabolic logistic equation, Obstacle problem, Positive solution, Increasing power, Subsolution and supersolution |
Classification： |
35B40, 35B09, 35K91 |
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