On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation

الملخص EN

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.