Asymptotic behaviour of solutions for nonlinear diffusion equation with periodic absorption. (English) Zbl 0987.35086
Chen, 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 , , is a bounded domain in with smooth boundary, is smooth, strictly positive and periodic in time with period , and 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.
|35K65||Parabolic equations of degenerate type|
|34B40||Boundary value problems for ODE on infinite intervals|
|35K20||Second order parabolic equations, initial boundary value problems|
|35B10||Periodic solutions of PDE|