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Critical Exponents of Quasilinear Parabolic Equations

✍ Scribed by Yuan-Wei Qi; Ming-Xing Wang

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 138 KB
Volume: 267
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7771

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✦ Synopsis

In this paper we study the critical exponents of the Cauchy problem in R n of the quasilinear singular parabolic equations: u t = div ∇u m-1 ∇u + t s x σ u p , with non-negative initial data. Here s ≥ 0 n -1 / n + 1 < m < 1 p > 1 and σ > n 1 -m -1 + m + 2s . We prove that p c ≡ m + 1 + m + 2s + σ /n > 1 is the critical exponent. That is, if 1 < p ≤ p c then every non-trivial solution blows up in finite time, but for p > p c , a small positive global solution exists.  2002 Elsevier Science (USA)

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