The Global Attractor For A Class Of Nonlinear Evolution Equation

Investigations on the existence of the global attractor for the nonlinear evolution equations, which are arisen from the fields of mathematics and branches of science (physics, mechanics and biology, etc), not only have great significances in theory, but also have wide applications in practice. During the past years, much research interest has focus on the nonlinear evolution equations since their widely application in practice, complexity and challenges in the theoretical study.This thesis is devoted to study the existence of the global attractor for a class of nonlinear evolution equations which is mixed by the nerve conductive equation and nonlinear wave equation. The specific form of the equation, initial and boundary conditions are utt-c02(σ(▽u))x-γ△ut-β△utt=-f(x,t,u,▽u,ut,▽ut)ut-g(x,t,u,▽u,ut,▽ut), u(x,0)=u0(x),u,(x,0)=u1(x) u|(?)Ω＝0, where Q is a bounded domain in R with a smooth boundary (?)Ω, c0,γ,β are given constants (see [9]),ρ,f,g are given real functions.This paper is organized as follows:In the first chapter, we mainly introduce the present research situation of the nerve conductive equation and nonlinear wave equation, then illustrate the content of this paper.In the second chapter, we give some related concepts and basic lemmas which are used in this paper.In the third chapter, we study the existence and uniqueness of the global strong solution for the nerve conductive and nonlinear wave mixed equation.In the fourth chapter, we prove the existence of attractor for the mixed equation.In the fifth chapter, we summarize the full text and propose some prospects.