I'm trying to use Mathematica to solve the following equation $$\partial_t u = \partial_x (u^2 \partial_xu)$$ with $$u(0,t)=u(1,t)=0$$ and $$u_0(x)=\sin(\pi x)$$ in order to check a numerical method I developed with Python. What I obtain at time $t=1$ with Python is the following one:
I want to use Mathematica to see whether its solution is the same I obtain or not, but since I'm not familiar, I can't do that and I need a check.
Any confirm or check is highly appreciated !