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2009, 2009(Special): 691-696. doi: 10.3934/proc.2009.2009.691

A remark on blow-up at space infinity

Yukihiro Seki 1,

1. 

Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan

Received  July 2008 Revised  July 2009 Published  September 2009

In this note we discuss blow-up at space infinity for quasilinear parabolic equation $u_t = \Delta u^m + u^{p}$. It is known that if initial data is not a constant and takes its maximum at space infinity in a certain sense, the solution blows up only at space infinity at minimal blow-up time. We show that if $m \ge 1$ and a solution blows up at minimal blow-up time, then it blows up completely at the blow-up time.
Keywords: minimal blow-up time, complete blow-up, Blow-up at space infinity.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Yukihiro Seki. A remark on blow-up at space infinity. Conference Publications, 2009, 2009 (Special) : 691-696. doi: 10.3934/proc.2009.2009.691
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