Self-similar solutions of the \(p\)-Laplace heat equation: the fast diffusion case (Q996139)

This fundamental treatise contains a complete description of the self-similar solutions of the equation \(u_t-\text{div} (| \nabla u| ^p-2\nabla u)=0\) in the fast diffusion case (i.e. \(p\in (1, 2)\)). The list consists of signed solution of the form \(u(x,t)=(\pm t)^{-\alpha\setminus \beta w((\pm t)^{-1/\beta}| x| )} \) with \(\alpha\), \(\beta\) real, \(\beta\neq 0\), regular or singular at \(x=0\), and possibly not defined on all of \({\mathbb R}^N\times (0, \infty)\).