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Zbl 1221.35076
Yamauchi, Yusuke
Life span of solutions for a semilinear heat equation with initial data having positive limit inferior at infinity. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 15, 5008-5014 (2011). ISSN 0362-546X

Summary: We present a new upper bound of the life span of positive solutions of a semilinear heat equation for initial data having positive limit inferior at space infinity. The upper bound is expressed by the data in limit inferior, not in every direction, but around a specific direction. It is also shown that the minimal time blow-up occurs when initial data attains its maximum at space infinity.

MSC 2000:: *35B44
35K57 Reaction-diffusion equations
35K58
35B09

Keywords: upper bound of life span

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