International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 1, Pages 35-44
doi:10.1155/S0161171201003581
Asymptotic behaviour of solutions for porous medium equation with periodic absorption
1Department of Mathematics, Jilin University, Changchun 130012, China
2Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China
Received 28 June 1999
Copyright © 2001 Yin Jingxue and Wang Yifu. 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
This paper is concerned with porous medium equation with periodic absorption. We are interested in the discussion of asymptotic behaviour of solutions of the first boundary value problem for the equation. In contrast to the equation without sources, we show that the solutions may not decay but may be “attracted” into any small neighborhood of the set of all nontrivial periodic solutions, as time tends to infinity. As a direct consequence, the null periodic solution is “unstable.” We have presented an accurate condition on the sources for solutions to have such a property. Whereas in other cases of the sources, the solutions might decay with power speed, which implies that the null periodic solution is “stable.”