Boundary Value Problems
Volume 2009 (2009), Article ID 415709, 16 pages
Research Article

Existence and Uniqueness of Very Singular Solution of a Degenerate Parabolic Equation with Nonlinear Convection

School of Mathematical Sciences, Ocean University of China, Qingdao, 266-071, China

Received 22 October 2008; Revised 24 February 2009; Accepted 8 April 2009

Academic Editor: Ugur Abdulla

Copyright © 2009 Zhong Bo Fang et al. 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 here investigate the existence and uniqueness of the nontrivial, nonnegative solutions of a nonlinear ordinary differential equation: (|f|p2f)+βrf+αf+(fq)=0 satisfying a specific decay rate: limrrα/βf(r)=0 with α:=(p1)/(pq2p+2) and β:=(qp+1)/(pq2p+2). Here p>2 and q>p1. Such a solution arises naturally when we study a very singular self-similar solution for a degenerate parabolic equation with nonlinear convection term ut=(|ux|p2ux)x+(uq)x defined on the half line [0,+).