Blow-up and extinction of solutions to a fast diffusion equation with homogeneous Neumann boundary conditions
Jian Li, Yuzhu Han, Haixia Li · DOAJ (DOAJ: Directory of Open Access Journals) · 2016
In this article, we study blow-up and extinction properties of solutions to a fast diffusion $p$-Laplace equation with a nonlocal term under homogeneous Neumann boundary conditions. We first show that the solutions with positive initial energy will blow up in finite time, and then give some sufficient conditions for the solutions to vanish in finite time, using the method of integral estimates. Moreover, the decay rates near the extinction time are also derived.