Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities

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• 作者：Philippe Souplet^a ; ^{souplet@math.univ-paris13.fr" class="auth_mail" title="E-mail the corresponding author} ; Slim Tayachi^b ; ^{slim.tayachi@fst.rnu.tn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 35B40 ; 35B45 ; 35B50 ; secondary ; 35K60 ; 35K57
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：138
• 期：Complete
• 页码：428-447
• 全文大小：666 K

文摘

We study positive blowing-up solutions of systems of the form: with b4078923a5c" title="Click to view the MathML source">δ₁,δ₂>0${\delta }_1,{\delta }_2>0$ and p,q>0$p,q>0$. We prove single-point blow-up for large classes of radially decreasing solutions. This answers a question left open in a paper of Friedman and Giga (1987), where the result was obtained only for the equidiffusive case δ₁=δ₂${\delta }_1={\delta }_2$ and the proof depended crucially on this assumption.