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

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.