Asymptotic behavior of degenerate logistic equations

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• 作者：José ; M. Arrieta^a ; ^b ; ^{arrieta@mat.ucm.es" class="auth_mail" title="E-mail the corresponding author} ; Rosa Pardo^a ; ^{rpardo@mat.ucm.es" class="auth_mail" title="E-mail the corresponding author} ; Aní ; bal Rodrí ; guez-Bernal^a ; ^b ; ^{arober@mat.ucm.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35B40 ; 35K58 ; 35B32 ; 35J61
• 刊名：Journal of Differential Equations
• 出版年：2015
• 出版时间：5 December 2015
• 年：2015
• 卷：259
• 期：11
• 页码：6368-6398
• 全文大小：463 K

文摘

We analyze the asymptotic behavior of positive solutions of parabolic equations with a class of degenerate logistic nonlinearities of the type 位u−n(x)u^蟻$位u-n(x)u^{蟻}$. An important characteristic of this work is that the region where the logistic term n(⋅)$n(\cdot )$ vanishes, that is $K_0=\{x:n(x)=0\}$, may be non-smooth. We analyze conditions on 位, 蟻  , n(⋅)$n(\cdot )$ and K₀$K_0$ guaranteeing that the solution starting at a positive initial condition remains bounded or blows up as time goes to infinity. The asymptotic behavior may not be the same in different parts of K₀$K_0$.