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

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

Year:    2004

Journal of Partial Differential Equations, Vol. 17 (2004), Iss. 4 : pp. 369–383

Abstract

In this paper we deal with the self-similar singular solution of the p-Laplacian evolution equation u_t = div(|∇|^{p-2}∇u) - |∇u|^q for p > 2 and q > 1 in R^n × (0, ∞). We prove that when p > q + n/(n + 1) there exist self-similar singular solutions, while p ≤ 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2004-JPDE-5399

Journal of Partial Differential Equations, Vol. 17 (2004), Iss. 4 : pp. 369–383

Published online:    2004-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    p-Laplacian evolution equation