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Critical exponents of quasilinear parabolic equations. (English) Zbl 1010.35005
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 $\sigma >n(1-m)-1-m-2s.$

35B33Critical exponents (PDE)
35K55Nonlinear parabolic equations
35K65Parabolic equations of degenerate type
Full Text: DOI
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