Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 827087, 12 pages
doi:10.1155/2009/827087
On the Cauchy problem of a quasilinear degenerate parabolic equation
Zongqi Liang
and Huashui Zhan
School of Science, Jimei University, Xiamen 361021, China
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.