Solving nonlinear PDE with customary boundary conditions

Hello Everybody.

I want to solve this PDE with boundary conditions: Ut=a.Uxx+b.(Ux)^2 where a and b are constants. U(x,0)=f(x) U(L,t)=0 Ux(0,t)=c.Ut(0,t)+d where c and d are constants. Any help would be highly appreciated.

Thanks in advance.