Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 87650, 8 pages
doi:10.1155/2007/87650
Research Article

Extinction and Decay Estimates of Solutions for a Class of Porous Medium Equations

Wenjun Liu,1,2 Mingxin Wang,1 and Bin Wu2

 1Department of Mathematics, Southeast University, Nanjing 210096, China
2College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China
Received 3 April 2007; Accepted 6 September 2007

Recommended by Michel Chipot

Abstract

The extinction phenomenon of solutions for the homogeneous Dirichlet boundary value problem of the porous medium equation ut=Δum+λ|u|p−1u−βu, 0<m<1, is studied. Sufficient conditions about the extinction and decay estimates of solutions are obtained by using Lp-integral model estimate methods and two crucial lemmas on differential inequality.