Abstract and Applied Analysis
Volume 2005 (2005), Issue 2, Pages 87-94
doi:10.1155/AAA.2005.87
Blow-up of solutions of a semilinear heat equation with a
memory term
Mathematical Sciences Department, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Received 26 May 2004
Copyright © 2005 Salim A. Messaoudi. 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
We consider an initial
boundary value problem related to the equation ut−Δu+∫0tg(t−s)Δu(x,s)ds=|u|p−2u and prove, under suitable conditions on g and p,
a blow-up result for certain solutions with positive initial energy.