Global Attractors For Two Kinds Of Coupled Beam Equations Under Nonlinear Boundary Conditions

In this paper,we mainly discuss the long-time dynamic behavior of solutions of two kinds of coupled equations 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,initial boundary value problems for some nonlinear elastic beams and the main work in this paper.The second chapter,we introduce mainly the basic definitions,common inequalities and basic lemmas used in this paper.The three chapter,we study the global attractor of thermoelastic coupled beam equations under nonlinear boundary conditions.First,by priori estimates and common inequalities,we obtain:when the initial value satisfies(u0,u1,?0 ? V1 × L2 × L2,the system(3.0.1)-(3.0.3)exists a unique weak solution;when the initial value satisfies(u0,u1,?0)? W1 × W1 × H02,the systems(3.0.1)-(3.0.3)exists a unique regular solution;Secondly,there exists 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 a coupled beam equations with the rotational inertia and the structural damping under nonlinear boundary conditions.First,by priori estimates and common inequalities,we obtain:when the initial value satisfies(u0,u1,v0,v1)? V2× U2 × V2×U2,the system(4.0.1)-(4.0.3)exists a unique weak solution;when the initial value satisfies(u0,u1,v0,v1)? W2 × W2 × W2 × W2,the system(4.0.1)-(4.0.3)exists a unique regular solution;Secondly,there exists the global attractor for the weak solu-tion,through the existence of a bounded absorbing set and the asymptotic smoothness of the semigroup of the system.The five chapter,we summarize the full text and prospects...