Global Attractor For A Class Of Coupled Beam Equations

The coupled beam equation with memory term has become a very active topic in the field of partial differential equations,and it has been paid more and more attention by scholars at home and abroad.After considering the nonlinear and memory terms,this article discusses the initial boundary value problem for a class of coupled beam equations.The equations are as follows:(?)With the initial condition u(x,0)=u0(x),ut(x,0)=u1(x),?(x,0)=?0(x).With the boundary condition(?) where ? is the closed interval[0,l],?1,?2?1,?,?,?,T>0,h>2 is constant.There are five chapters in this thesis:In chapter 1 gives the research background,present situation and main work of this article.In chapter 2 introduces the basic definitions,important lemmas and basic assumptions used in this article.In chapter 3 proves the existence and uniqueness of the integral solution of the coupled beam equations.In chapter 4 studies the existence of global attractors of the equations.In chapter 5 summarizes the full text and brings out some expectations.