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2004 Instantaneous shrinking of the support in degenerate parabolic equations with strong absorption
Michael Winkler
Adv. Differential Equations 9(5-6): 625-643 (2004).

Abstract

We investigate the phenomenon of instantaneous shrinking of the support of nonnegative solutions to the Cauchy problem in $\\mathbb R^n$ for $$ u_t=f(u) \Delta u - g(u), \quad \mbox{where } f(0)=0. $$ Among other results, it is shown by means of comparison and integral techniques that under some structural assumptions on $f$ and $g$, a necessary {\em and} sufficient condition on the growth of $g$ near zero for instantaneous shrinking to occur is $\int_0^1 \frac{ds}{g(s)} <\infty$.

Citation

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Michael Winkler. "Instantaneous shrinking of the support in degenerate parabolic equations with strong absorption." Adv. Differential Equations 9 (5-6) 625 - 643, 2004.

Information

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

zbMATH: 1101.35010
MathSciNet: MR2099974

Subjects:
Primary: 35K55
Secondary: 35B05, 35B40, 35K65

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.9 • No. 5-6 • 2004
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