Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 827087, 12 pages
doi:10.1155/2009/827087
Research Article

On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation

Zongqi Liang and Huashui Zhan

School of Science, Jimei University, Xiamen 361021, China

Received 21 April 2009; Accepted 25 August 2009

Academic Editor: Guang Zhang

Copyright © 2009 Zongqi Liang and Huashui Zhan. 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.

Abstract

By Oleinik's line method, we study the existence and the uniqueness of the classical solution of the Cauchy problem for the following equation in [0,T]×R2: ∂xxu+u∂yu−∂tu=f(⋅,u), provided that T is suitable small. Results of numerical experiments are reported to demonstrate that the strong solutions of the above equation may blow up in finite time.