Solutions with snaking singularities for the fast diffusion equation

Abstract

We construct solutions of the fast diffusion equation, which exist for all $t\in \mathbb{R}$ and are singular on the set $\Gamma (t):=\{\xi (s);-\infty <s\le ct\}$, $c>0$, where $\xi \in C^3(\mathbb{R};{\mathbb{R}}^n)$, $n\ge 2$. We also give a precise description of the behavior of the solutions near $\Gamma (t)$.

To appear in Transactions of the American Mathematical Society