Self-similar Singular Solution of a P-Laplacian Evolution Equation with Gradient Absorption Term

Abstract

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In this paper we deal with the self-similar singular solution of the p-Laplacian evolution equation u_t = div(|\u2207|^{p-2}\u2207u) - |\u2207u|^q for p > 2 and q > 1 in R^n \u00d7 (0, \u221e). We prove that when p > q + n\/(n + 1) there exist self-similar singular solutions, while p \u2264 q+n\/(n+1) there is no any self-similar singular solution. In case of existence, the self-similar singular solutions are the self-similar very singular solutions, which have compact support. Moreover, the interface relation is obtained.<\/p>"