TITLE

Singular solutions of some nonlinear parabolic equations with spatially inhomogeneous absorption

AUTHOR(S)
Shishkov, Andrey; V�ron, Laurent
PUB. DATE
November 2008
SOURCE
Calculus of Variations & Partial Differential Equations;Nov2008, Vol. 33 Issue 3, p343
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We study the limit behaviour of solutions of $${{\partial_t} u- \Delta u + h(|x|) |u|^{p-1}u = 0\,in\,{\mathbb{R}}^N \times (0,T)}$$ with initial data k d 0 when k ? 8, where h is a positive nondecreasing function and p > 1. If h( r) = r � , � > N( p - 1) - 2, we prove that the limit function u 8 is an explicit very singular solution, while such a solution does not exist if � = N( p - 1) - 2. If lim inf r? 0 r 2 ln (1/ h( r)) > 0, u 8 has a persistent singularity at (0, t) ( t = 0). If $${\int_{0}^{r_{0}}r\ln (1/h(r))\,dr < \infty}$$ , u 8 has a pointwise singularity localized at (0, 0).
ACCESSION #
33532989

 

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