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Volume 17, Issue 4
Self-similar Singular Solution of a P-Laplacian Evolution Equation with Gradient Absorption Term

Peihu Shi

J. Part. Diff. Eq., 17 (2004), pp. 369-383.

Published online: 2004-11

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  • 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.

  • Keywords

p-Laplacian evolution equation gradient absorption self-similar singular solution very singular solution

  • AMS Subject Headings

35K15 35K65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-17-369, author = {}, title = {Self-similar Singular Solution of a P-Laplacian Evolution Equation with Gradient Absorption Term}, journal = {Journal of Partial Differential Equations}, year = {2004}, volume = {17}, number = {4}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5399.html} }
TY - JOUR T1 - Self-similar Singular Solution of a P-Laplacian Evolution Equation with Gradient Absorption Term JO - Journal of Partial Differential Equations VL - 4 SP - 369 EP - 383 PY - 2004 DA - 2004/11 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5399.html KW - p-Laplacian evolution equation KW - gradient absorption KW - self-similar KW - singular solution KW - very singular solution AB -

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.

Peihu Shi . (2019). Self-similar Singular Solution of a P-Laplacian Evolution Equation with Gradient Absorption Term. Journal of Partial Differential Equations. 17 (4). 369-383. doi:
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