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2004 Spectra of critical exponents in nonlinear heat equations with absorption
V. A. Galaktionov, P. J. Harwin
Adv. Differential Equations 9(3-4): 267-298 (2004).

Abstract

It has been known from the beginning of the 1980's that the global $L^1$ solutions of the classical porous medium equation with absorption $u_t = \Delta u^m - u^p$ in $\mathbb R^N \times \mathbb R_+$, with $m,p>1$ change their large-time behavior at the critical absorption exponent $p_0=m+2/N$. We show that, actually, there exists an infinite sequence $\{p_k, \, k \ge 0\}$ of critical exponents generating a countable subset of different non-self-similar asymptotic patterns. The results are extended to the fully nonlinear dual porous-medium equation with absorption.

Citation

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V. A. Galaktionov. P. J. Harwin. "Spectra of critical exponents in nonlinear heat equations with absorption." Adv. Differential Equations 9 (3-4) 267 - 298, 2004.

Information

Published: 2004
First available in Project Euclid: 18 December 2012

zbMATH: 1122.35014
MathSciNet: MR2100629

Subjects:
Primary: 35K55
Secondary: 35B33, 35B40, 47N20

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.9 • No. 3-4 • 2004
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