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2005 Universal bounds at the blow-up time for nonlinear parabolic equations
Daniele Andreucci, Anatoli F. Tedeev
Adv. Differential Equations 10(1): 89-120 (2005).

Abstract

We prove a priori supremum bounds for solutions to \begin{equation*} u_{t} - {\text{\rm div}} \big(u^{m-1} | {Du}| ^{\lambda -1} Du \big) = f(x) u^{p}\,, \end{equation*} as $t$ approaches the time when $u$ becomes unbounded. Such bounds are universal in the sense that they do not depend on $u$. Here $f$ may become unbounded, or vanish, as $x\to 0$. When $f\equiv1$, we also prove a bound below, as well as uniform localization of the support, for subsolutions to the corresponding Cauchy problem.

Citation

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Daniele Andreucci. Anatoli F. Tedeev. "Universal bounds at the blow-up time for nonlinear parabolic equations." Adv. Differential Equations 10 (1) 89 - 120, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1122.35042
MathSciNet: MR2106122

Subjects:
Primary: 35K55
Secondary: 35B40

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.10 • No. 1 • 2005
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