Abstract and Applied Analysis
Volume 2013 (2013), Article ID 747613, 5 pages
http://dx.doi.org/10.1155/2013/747613
Research Article

Extinction and Nonextinction for the Fast Diffusion Equation

Chunlai Mu,1 Li Yan,1,2 and Yi-bin Xiao3

1College of Mathematics and Physics, Chongqing University, Chongqing 400044, China
2College of Elementary Education, Chongqing Normal University, Chongqing 400047, China
3School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China

Received 28 February 2013; Accepted 28 April 2013

Academic Editor: Ru Dong Chen

Copyright © 2013 Chunlai Mu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with the extinction and nonextinction properties of the fast diffusion equation of homogeneous Dirichlet boundary condition in a bounded domain of with . For , under appropriate hypotheses, we show that is the critical exponent of extinction for the weak solution. Furthermore, we prove that the solution either extinct or nonextinct in finite time depends strongly on the initial data and the first eigenvalue of with homogeneous Dirichlet boundary.