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A critical exponent in a degenerate parabolic equation

✍ Scribed by Michael Winkler

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 145 KB
Volume: 25
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.319

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✦ Synopsis

Abstract

We consider positive solutions of the Cauchy problem in \documentclass{article}\usepackage{amsfonts}\begin{document}\pagestyle{empty}$\mathbb{R,}^n$\end{document} for the equation

$$u_t=u^p,\Delta u+u^q,\quad p\geq1,; q\geq 1$$\nopagenumbers\end
and show that concerning global solvability, the number q = p + 1 appears as a critical growth exponent. Copyright © 2002 John Wiley & Sons, Ltd.

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