## Abstract and Applied Analysis

### Extinction and Nonextinction for the Fast Diffusion Equation

#### 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 ${R}^{N}$ with $N>2$. For $0, under appropriate hypotheses, we show that $m=p$ 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 $-\mathrm{\Delta }$ with homogeneous Dirichlet boundary.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 747613, 5 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393444388

Digital Object Identifier
doi:10.1155/2013/747613

Mathematical Reviews number (MathSciNet)
MR3055982

Zentralblatt MATH identifier
1275.35029

#### Citation

Mu, Chunlai; Yan, Li; Xiao, Yi-bin. Extinction and Nonextinction for the Fast Diffusion Equation. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 747613, 5 pages. doi:10.1155/2013/747613. https://projecteuclid.org/euclid.aaa/1393444388

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