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

Boundary Value Problems20092009:415709

Received: 22 October 2008

Accepted: 8 April 2009

Published: 5 May 2009


We here investigate the existence and uniqueness of the nontrivial, nonnegative solutions of a nonlinear ordinary differential equation: satisfying a specific decay rate: with and . Here and . Such a solution arises naturally when we study a very singular self-similar solution for a degenerate parabolic equation with nonlinear convection term defined on the half line .


Differential EquationPartial Differential EquationOrdinary Differential EquationFunctional EquationParabolic Equation

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Authors’ Affiliations

School of Mathematical Sciences, Ocean University of China, Qingdao, China


© Zhong Bo Fang et al. 2009

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.