Uniform Exponential Attractors For Three Kinds Of Non-autonomous Infinite Lattice Systems

Nonlinear schrodinger equation、long-wave-short-wave resonance equations and stro-ngly damped wave equation are important partial differential equations in the quantum me-chanics、plasma physics and classical physics respectively. Non-autonomous nonlinear schrodinger equation、non-autonomous long-wave-short-wave resonance equations and non-autonomous strongly damped wave equation at the discretization of high dimensional space can be regarded as the discrete analogue of the continuously non-autonomous cor-responding equation(s) respectively, can also be regarded as first order or second order infinite lattice systems、this thesis research the long time behavior of solutions for non-autonomous nonlinear schrodinger equation、non-autonomous long-wave-short-wave res-onance equations and non-autonomous strongly damped wave equation at the discretization of high dimensional space, and then respectively obtain the existence of uniform exponen-tial attractors for the corresponding equation(s).In Chapter1,We firstly introduce the relevant knowledge of the infinite dimensional dynamical system and the infinite lattice system. Secondly on the basic of introducing the physical background of three kinds of above-mentioned equation(s) and summarizing related research progress, we summarize the main work of this thesis.we finally give frequently-used inequalities and relevant definitions involved in the thesis.In Chapter2、Chapter3and Chapter4, we respectively consider the existence of uniform exponential attractors for non-autonomous nonlinear schrodinger equation、non-autonomous long-wave-short-wave resonance equations and non-autonomous strongly da-mped wave equation at the discretization of high dimensional space.we firstly introduced the background of the research model. We secondly prove the existence and uniqueness of solutions and the existence of uniform bounded absorbing sets for the processes. We finally prove the Lipschitz continuity of the corresponding solution semigroup and obtain the existence of uniform exponential attractors for the family of processes associated with the studied lattice dynamical systems.