The Study Of Attractor On Several Kinds Of Equation(Equations) System Of Complex Elastic Beam Structure

In this paper,for four kinds of complex elastic beam equation(equations)system,we studied the initial boundary value problem and the existence of attractor which is the most essential concept of longtime dynamical behavior on infinite dimension dynamical system.First of all,using the Galerkin method combining some priori estimates and in-equalities skill and the Sobolev space theory and so on,we gave the existence and uniqueness of global solutions of four kinds of different systems,then we defined the semigroups of three different types of autonomous infinite dimensional dynamical sys-tems and a process family of two parameter for a class of non autonomous infinite dimensional dynamical system;Secondly,by priori estimates combined with some skills of inequality,we gave the bounded absorbing sets of the three different types of au-tonomous infinite dimensional dynamical systems and the uniform bounded absorbing set of a class of non autonomous infinite dimensional dynamical systems determined by complex elastic beam structure;Finally,we proved that the corresponding solu-tion semigroups of three kinds of autonomous infinite dimensional dynamical systems is asymptotically smooth and a process family of two parameter of a class of non au-tonomous infinite dimensional dynamical system processes is uniform asymptotically compact.Furthermore,according to existence theorems of the global attractor and the uniform attractor we proved the existence of the global attractor of two kinds of thermoelasticity coupled equation with structure damping and a kind of elastic beam equation system under nonlinear boundary conditions,and the existence of the uniform attractor of a kind of elastic beam equation non-autonomous system under nonlinear boundary conditions determined by complex elastic beam structure.The specific con-tents are as follows:1.In the first chapter we introduced the necessity of the study and the research status of attractor,and the current research situation of infinite dimensional dynamical system determined by elastic beam structure2.In the second chapter we introduced some basic definitions and some basic inequalities and some basic lemmas used by this paper.3.In the third chapter we gave the the initial boundary value system and existence of global attractor of system on the n-dimensional thermoelastic coupled beam equations with damping structure under the homogeneous boundary conditions and the initial conditions4.In the fourth chapter,for thermoelastic coupled beam equations with a thermal memory under the homogeneous boundary conditions and the initial conditions of the system,by introducing a a new weighted space,we translated the non autonomous system into autonomous system,and we gave the existence of the global solution and the global attractor.5.In the fifth chapter we gave the existence of global solutions and global attractor of system on a single elastic beam equation with structural damping under the nonlinear boundary conditions and under certain initial conditions.6.The sixth chapter gave the existence of uniform bounded absorbing set and uniform attractor for the system on non autonomous single elastic beam equation with local damping under the nonlinear boundary conditions and under certain initial conditions.