Electron. J. Differential Equations, Vol. 2016 (2016), No. 236, pp. 1-10.

Blow-up and extinction of solutions to a fast diffusion equation with homogeneous Neumann boundary conditions

Jian Li, Yuzhu Han, Haixia Li

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.

Submitted June 2, 2016. Published August 29, 2016.
Math Subject Classifications: 35K55, 35B40.
Key Words: Blow-up; extinction; non-extinction; Neumann boundary condition.

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Jian Li
Information Technology College
Jilin Agricultural University
Changchun 130118, China
email: liemperor@163.com
Yuzhu Han
School of Mathematics
Jilin University
Changchun 130012, China
email: yzhan@jlu.edu.cn
Haixia Li
School of Mathematics
Changchun Normal University
Changchun 130032, China
email: lihaixia0611@126.com

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