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2007 On bounds for global solutions of semilinear parabolic equations with critical and subcritical Sobolev exponent
Michinori Ishiwata
Differential Integral Equations 20(9): 1021-1034 (2007).

Abstract

In this paper, we are concerned with the existence of $L^\infty$-global bounds for global-in-time solutions of some semilinear parabolic problems. It is well known that every global-in-time solution for the subcritical problem is globally bounded in $L^\infty$, while there exists a global solution which is not bounded in $L^\infty$ globally in time in the critical case. In this paper, we discuss the necessary and sufficient condition for the existence of $L^\infty$-global bounds, which is valid for the subcritical and the critical case in a unified way. Moreover, using our main results, we provide various examples with the critical exponent in which every global-in-time solution has an $L^\infty$-global bound.

Citation

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Michinori Ishiwata. "On bounds for global solutions of semilinear parabolic equations with critical and subcritical Sobolev exponent." Differential Integral Equations 20 (9) 1021 - 1034, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35212
MathSciNet: MR2349378

Subjects:
Primary: 35K55
Secondary: 35B33 , 35B45

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 9 • 2007
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