On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation. (27th September 2009) - Liang, Zongqi; Zhan, Huashui
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 ] × R 2 :∂ x x u + u ∂ y u − ∂ t u = f ( ⋅, u ), provided thatT 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.