Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Extinction and Decay Estimates of Solutions for a Class of Porous Medium Equations | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 87650 8 pages doi 2007 87650 Research Article Extinction and Decay Estimates of Solutions for a Class of Porous Medium Equations Wenjun Liu Mingxin Wang and Bin Wu Received 3 April 2007 Accepted 6 September 2007 Recommended by Michel Chipot The extinction phenomenon of solutions for the homogeneous Dirichlet boundary value problem of the porous medium equation ut Ảum A u p 1u u 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. Copyright 2007 Wenjun Liu et al. 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. 1. Introduction and main results This paper is devoted to the extinction and decay estimates for the porous medium equation ut Aum A u p 1u ỉu x e o t 0 u x t 0 x e do t 0 u x 0 u0 x 0 x e o with 0 m 1 and p A 0 where o c RN N 2 is a bounded domain with smooth boundary. The phenomenon of extinction is an important property of solutions for many evolutionary equations which have been studied extensively by many researchers. Especially there are also some papers concerning the extinction for the porous medium equation. For instance in 1-3 the authors studied the extinction and large-time behavior of solution of for the case 0 and A 0 and in 4 the authors obtained conditions for the extinction of solutions of without absorption by using sub- and supersolution 2 Journal of Inequalities and Applications methods and an eigenfunction argument. But as far as we know few works are concerned with the decay estimates of solutions for the porous medium equation. The existence and uniqueness of nonnegative solution for problem - have been
