Asymptotic behaviour of solutions for nonlinear diffusion equation with periodic absorption.

*(English)*Zbl 0987.35086Chen, Hua (ed.) et al., Partial differential equations and their applications. Proceedings of the conference, Wuhan, China, April 5-9, 1999. Singapore: World Scientific. 305-308 (1999).

The article is devoted to studying a nonlinear diffusion equation with periodic absorption of the form

where $m>1$, $\alpha \ge 1$, ${\Omega}$ is a bounded domain in ${\mathbb{R}}^{N}$ with smooth boundary, $a(x,t)$ is smooth, strictly positive and periodic in time with period $\omega >0$, and ${u}_{0}\left(x\right)$ is smooth and nonnegative. The aim of the article under review is to prove the existence of an attractor which consists of all nontrivial periodic solutions. In addition, the authors discuss the asymptotic behaviour of a multidimensional nonlinear diffusion equation.

Reviewer: Vladimir N.Grebenev (Novosibirsk)