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

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.