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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

t u=Δ(u m )+a(x,t)u α inΩ×(0,),u(x,t)=0onΩ×(0,),u(x,0)=u 0 (x)inΩ,

where m>1, α1, Ω is a bounded domain in N with smooth boundary, a(x,t) is smooth, strictly positive and periodic in time with period ω>0, and u 0 (x) 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.

35K65Parabolic equations of degenerate type
35B41Attractors (PDE)
34B40Boundary value problems for ODE on infinite intervals
35K20Second order parabolic equations, initial boundary value problems
35B10Periodic solutions of PDE