✦ LIBER ✦

Global existence and blowup of a localized problem with free boundary

✍ Scribed by Peng Zhou; Jie Bao; Zhigui Lin

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 260 KB
Volume: 74
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2010.11.047

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✦ Synopsis

This paper is concerned with a double fronts free boundary problem for the heat equation with a localized nonlinear reaction term. The local existence and uniqueness of the solution are given by applying the contraction mapping theorem. Then we present some conditions so that the solution blows up in finite time. Finally, the long-time behavior of the global solution is discussed. We show that the solution is global and fast if the initial data is small and that a global slow solution is possible when the initial data is suitably large.

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