nonlinear time dependent PDE

Does anybody know how to solve the following nonlinear time dependent PDE?

Du/Dt+(u*Du/Dx)^2+(u^3)*D^2(u)/Dx^2+u^3;
initial condition:
u0=0
boundary conditions:
at x=0 ==> Du/Dx=10;
at x=1==> Du/Dx=0;
Any help or suggestions would be appreciated

Answer 1

[Torsten]

Try MATLAB's "pdepe".

Best wishes

Torsten.