Global Attractor Of Coupled Bending And Torsion Beam Equations Under Nonlinear Boundary Conditions

In this paper,we mainly study the global attractor of two types of coupled bending and torsion beam equations with linear damping and nonlinear damping terms under nonlinear boundary conditions.The structure of this paper is as follows:The first chapter,we introduce briefly the background of infinite dimensional dynamical systems and the research progress of the existence of the global attractor of the beam equation.The second chapter,we introduce mainly the basic definitions,basic lemmas and common inequalities in this paper.The three chapter,we study the global attractor of the coupled beam equations with linear damping term under nonlinear boundary conditions.First,by the Galerkin method and priori estimations,inequality techniques and Sobolev space theories,we obtain a unique regular solution;According to the denseness theory,we obtain a unique weak solution of the system;Secondly,we consider the existence of the global attractor for the weak solution,through the existence of a bounded absorbing set and the asymptotic smoothness of the semigroup of the system.The four chapter,we study the global attractor of the coupled beam equations with nonlinear damping term under nonlinear boundary conditions.First,we proved the existence and uniqueness of global solution by the Galerkin method.Secondly,we proved the system has a bounded absorbing set and asymptotic smooth of the related solution semigroup.Finally get the existence of the global attractor.The proof steps are similar to the previous chapter,and the special point is the ingenious treatment of nonlinear terms M(·),N(·)in this process.The five chapter,we summarize the full text and put forward prospects.