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arXiv · 1206.6089

Increasing powers in a degenerate parabolic logistic equation

José Francisco Rodrigues·Hugo Tavares
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Abstract

The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem $$ \partial_t u-Δu=a u-b(x) u^p \text{in} Ω\times \R^+, u(0)=u_0, u(t)|_{\partial Ω}=0 $$ as $p\to +\infty$, where $Ω$ is a bounded domain and $b(x)$ is a nonnegative function. We deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards we fully describe its long time behavior.

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José Francisco Rodrigues, Hugo Tavares. 2012-06-26. Increasing powers in a degenerate parabolic logistic equation. https://arxiv.org/abs/1206.6089

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