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2007 Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent
Marek Fila, John R. King, Michael Winkler, Eiji Yanagida
Adv. Differential Equations 12(1): 1-26 (2007).

Abstract

We consider the Cauchy problem for a semilinear parabolic equation with a nonlinearity which is critical in the Joseph-Lundgren sense. We find the grow-up rate of solutions that approach a singular steady state from below as $t\to\infty$. The grow-up rate in the critical case contains a logarithmic term which does not appear in the Joseph-Lundgren supercritical case, making the calculations more delicate.

Citation

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Marek Fila. John R. King. Michael Winkler. Eiji Yanagida. "Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent." Adv. Differential Equations 12 (1) 1 - 26, 2007.

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1170.35456
MathSciNet: MR2272819

Subjects:
Primary: 35K55
Secondary: 35B33, 35B40, 35K15

Rights: Copyright © 2007 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.12 • No. 1 • 2007
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