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A remark on blow-up at space infinity

Pages: 691 - 696, Issue Special, September 2009

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Yukihiro Seki - Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan (email)

Abstract: 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:  Blow-up at space infinity, minimal blow-up time, complete blow-up
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35

Received: July 2008;      Revised: July 2009;      Published: September 2009.