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May 2013 Life span of solutions for a quasilinear parabolic equation with initial data having positive limit inferior at infinity
Takefumi Igarashi
Proc. Japan Acad. Ser. A Math. Sci. 89(5): 63-67 (May 2013). DOI: 10.3792/pjaa.89.63

Abstract

We present a new upper bound of the life span of positive solutions of a quasilinear parabolic equation for the 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 the initial data attain its maximum at space infinity.

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Takefumi Igarashi. "Life span of solutions for a quasilinear parabolic equation with initial data having positive limit inferior at infinity." Proc. Japan Acad. Ser. A Math. Sci. 89 (5) 63 - 67, May 2013. https://doi.org/10.3792/pjaa.89.63

Information

Published: May 2013
First available in Project Euclid: 30 April 2013

zbMATH: 1282.35090
MathSciNet: MR3049918
Digital Object Identifier: 10.3792/pjaa.89.63

Subjects:
Primary: 35B44 , 35D30 , 35K15 , 35K59

Keywords: Blow-up , Cauchy problem , life span , quasilinear parabolic equation

Rights: Copyright © 2013 The Japan Academy

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Vol.89 • No. 5 • May 2013
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