Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 20438, 21 pages
Self-similar singular solution of doubly singular parabolic equation with gradient absorption term
1Department of Mathematics, Southeast University, Nanjing 210096, China
2Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, China
Received 6 February 2004; Revised 8 January 2005; Accepted 8 January 2005
Copyright © 2006 Peihu Shi and Mingxin Wang. 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.
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.