On Global Attractor For Weighted P-Laplacian Parabolic Equations With Boundary Degeneracy

In this master degree dissertation, we consider a class of weighted p-Laplacian parabolic equations with boundary degeneracy and Dirichlet boundary condition on a bounded smooth domainΩ(?) Rⁿ.where p > 2;α>β> 2; g∈L^∞(Ω): u₀∈L¹(Ω); the weighted functionα(x)∈C(?),α(x) > 0 inΩand degenerates to 0 on (?)Ω, besides, (?).We mainly prove the existence and uniqueness of global weak solutions and the existence of global attractors in L¹(Ω). At first, by using the approximate method, we obtain the existence of global weak solutions for the problem. Then, the attractor is established by means of the Sobolev compact embedding theorem. The equation considered here is much more general and the main conclusions of the paper extend the previous relevant results in a certain degree.This paper is divided into four chapters.In Chapter one, the background on the theory of dynamical systems , the development of p-Laplacian parabolic equations and the study on weighted p-Laplacian parabolic equations are introduced.In Chapter two, some preliminary results and definitions that we will use in this paper are presented.In Chapter three, the existence and uniqueness of weak solutions of the problem studied are proved.In Chapter four, by means of compact embedding theorem, the existence of global attractors is proved. Besides, some properties of the attractors are presented.