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Extinction and decay estimates of solutions for a porous medium equation with nonlocal source and strong absorption

Xianghui Xu1, Zhong B Fang2* and Su-Cheol Yi3

Author Affiliations

1 Department of Mathematics, Pusan National University, Busan, 609-735, Republic of Korea

2 School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, P.R. China

3 Department of Mathematics, Changwon National University, Changwon, 641-773, Republic of Korea

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Boundary Value Problems 2013, 2013:24 doi:10.1186/1687-2770-2013-24

Published: 5 March 2013

Abstract

In this paper, we investigate extinction properties of the solutions for the initial Dirichlet boundary value problem of a porous medium equation with nonlocal source and strong absorption terms. We obtain some sufficient conditions for the extinction of nonnegative nontrivial weak solutions and the corresponding decay estimates which depend on the initial data, coefficients, and domains.