Existence And Uniqueness Of Solutions For One Kind Of Euler-bernoulli Beam Coupling Lattice Systems And Asymptotic Behavior Of Solutions For This Lattice Systems

As an important object of study of nonlinear science,an infinite dimensional dynamical system has been widely used in many important areas and has extensive commercial prospect. In particular, lattice system as one of the center of the infinite dimensional dynamical system content, has been applied in the field of biological, mechanics, civil engineering, etc, and has received the widespread attention of scientists. Recently,the study of lattice system solution, especially on the existence and uniqueness and asymptotic behavior of solution of the research, has become a hot topic in the research of many scholars. Exponential attractor is used to describe the infinite dimensional dynamic system’s dynamics behavior for a long time that index attract a positive invariant set of orbit and contains the whole attractor. This paper consists of two parts.The first one is related the existence and uniqueness of solutions of fractional Euler-Bernoulli beam coupling lattice systems. The second one is concerned with the existence of exponential attractor for Euler- Bernoulli beam coupling lattice systems of integer order. This paper is organized as follows:In chapter 1, the background and research value of Euler- Bernoulli Beam coupling lattice systems are introduced,and the inequalities, basic definitions and theories that this paper need are given.In chapter 2, the existence and uniqueness of solutions of Euler- Bernoulli beam coupling lattice systems of fractional order are considered. First of all, Euler- Bernoulli beam lattice systems is effected by the thermal effect and is generalized to the fractionalorder form. So an exploration is made on initial value problem of the solutions of a class of fractional order Euler- Bernoulli beam coupling lattice systems.Further, by using the Banach fixed point theorem、the Schauder’s fixed point theorem and the contraction mapping principle, we prove the existence and uniqueness of the lattice system solutions.In chapter 3, exponential attractor is considered which as one of dynamics behavior for a long time of solutions of integer order Euler- Bernoulli beam coupling lattice systems. In the Hilbert space,according to operator semigroup theory,semigroup of solution operator exists the absorption of bounded closed set.Operator of solutions satisfy uniformly Lipschitz continuous. By the orthogonal decomposition of the solution,solution operator meets a specific inequalities. By using compression mapping principle and Gronwall inequality, the existence of exponential attractor of the integer order Euler Bernoulli beam coupling lattice system is proved.In chapter 4, this paper is summarized and looked ahead.