Open Access

Self-similar singular solution of doubly singular parabolic equation with gradient absorption term

Journal of Inequalities and Applications20062006:20438

https://doi.org/10.1155/JIA/2006/20438

Received: 6 February 2004

Accepted: 8 January 2005

Published: 6 February 2006

Abstract

We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term for , and in . By shooting and phase plane methods, we prove that when there exists self-similar singular solution, while there is no any self-similar singular solution. In case of existence, the self-similar singular solution is the self-similar very singular solutions which have compact support. Moreover, the interface relation is obtained.

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Authors’ Affiliations

(1)
Department of Mathematics, Southeast University
(2)
Department of Mathematics, Xuzhou Normal University

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Copyright

© Shi and Wang 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.