Blow-down and immediate onset of positivity in the Neumann problem for (super-)fast diffusion equations

Youshan Tao, Michael Winkler

For the degenerate parabolic equation $u_t=\nabla \cdot (u^{m-1}\nabla u)$, the homogeneous Neumann problem in smoothly bounded domains $\Omega \subset {\mathbb{R}}^n$ is considered in th…