Interaction between nonlinear diffusion and geometry of domain

Rolando Magnanini, Shigeru Sakaguchi

Let $\Omega$ be a domain in ${\mathbb{R}}^N$, where $N\ge 2$ and $\partial \Omega$ is not necessarily bounded. We consider nonlinear diffusion equations of the form ${\partial }_{t}u=\Delta \varphi (u)$. Let $…