Localized non-diffusive asymptotic patterns for nonlinear parabolic equations with gradient absorption

Details Localized non-diffusive asymptotic patterns for nonlinear parabolic equations with gradient absorption Localized non-diffusive asymptotic patterns for nonlinear parabolic equations with gradient absorption

2007-09-13

arxiv.org/abs/0709.2082v1

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s10884-007-9093-y

We study the large-time behaviour of the solutions $u$ of the evolution equation involving nonlinear diffusion and gradient absorption $\partial_t u - \Delta_p u + |\nabla u|^q=0$. We consider the problem posed for $x\in {\mathbb R}^N $ and $t>0$ with non-negative and compactly supported initial data. We take the exponent $p>2$ which corresponds to slow $p$-Laplacian diffusion, and the exponent $q$ in the superlinear range $1

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