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On critical exponents for some quasilinear parabolic equations

✍ Scribed by Howard A. Levine; Gary M. Lieberman; Peter Meier

Publisher: John Wiley and Sons
Year: 1990
Tongue: English
Weight: 381 KB
Volume: 12
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670120507

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✦ Synopsis

Abstract

We study the Cauchy problem for the quasilinear parabolic equation
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where p > 1 is a parameter and ψ is a smooth, bounded function on (1, ∞) with − ⩽ __s__ψ′(s)/ψ(s) ⩽ θ for some θ > 0. If 1 < p < 1 + 2/N, there are no global positive solutions, whereas if p > 1 + 2/N, there are global, positive solutions for small initial data.

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