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Zbl 1010.35005
Qi, Yuan-Wei; Wang, Ming-Xing
Critical exponents of quasilinear parabolic equations.
(English)
[J] J. Math. Anal. Appl. 267, No.1, 264-280 (2002). ISSN 0022-247X

The critical exponent for the global existence of positive solutions of the equation $$u_t = \text{div}(|\nabla u|^{m-1}\nabla u)+t^s|x|^\sigma u^p$$ in $\Bbb R^n$ is found for $s\ge 0$, $(n-1)/(n+1)<m<1$, $p>1$ and $\sigma >n(1-m)-1-m-2s.$
[Marek Fila (Bratislava)]
MSC 2000:
*35B33 Critical exponents
35K55 Nonlinear parabolic equations
35K65 Parabolic equations of degenerate type

Keywords: global existence; blow-up; positive solutions

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