Long - Time Behavior Of A Class Of Semilinear Strongly Damped Wave Equations

In this paper, we study the following semilinear strongly damped wave equations a>0is constant,where Ω(?) c R2is a bounded domain with smooth boundary (?)Ω,(?)Ω is the border of Ω.This article use some important inequalities,such as Holder inequality,Gronwall inequality and so on.Then Combine Galerkin method and integral estimation method to study the existence and uniqueness of the understanding. The existence of global solution is necessary for the whole attractor,so that using the integral inequality, Sobolev embedding theorem and attractor equivalence theorem to prove the existence of the whole attractor of the above problems in the product L2x H\space and get the existence condition of the attractor.Through that we discusse the long time behavior of damped wave equations in the two-dimensional case and use graphusing the Hadamard transformationm ethods,we get that when a sufficiently large,there is the existence of inertial manifolds of the wave equation.The first chapter mainly introduces the research background and actuality of strong nonlinear damped wave equation,The second chapter mainly introduced in this paper, by using some of the basic knowledge and the commonly used inequality,The third chapter mainly discusses the existence of strong nonlinear damped wave equations with attractorThe fourth chapter mainly discusses the strong nonlinear damped wave equation of the existence.