具有记忆项和非局部非线性项的板方程的整体吸引子  

Global Attractors for a Plate Equation with Memory and Nonlocal Nonlinearities

作　　者：张彩红 任永华 ZHANG Caihong;REN Yonghua(College of Mathematics,Taiyuan University of Technology,Yuci 030600,China)

机构地区：[1]太原理工大学数学学院,山西榆次030600

出　　处：《应用数学》2018年第4期904-913,共10页Mathematica Applicata

基　　金：国家自然科学基金(11172194);山西自然基金(2015011006)

摘　　要：本文研究具有记忆项和非局部非线性项的板方程.首先利用近似的Faedo-Galerkin方法证得方程在初边值条件下解的适定性定理;其次通过先验估计并结合常用不等式证明该系统存在有界吸收集;最后利用Sobolev紧嵌入和收缩函数的方法证得解半群的渐近紧性,从而得到该系统整体吸引子的存在性.In this paper, we investigate a plate equation with memory and nonlocal nonlinearities.Firstly, by using Faedo-Galerkin method, we prove the well-posedness of solutions under the initial and boundary value conditions. Secondly, by a priori estimate method and some inequality, the existence of the boundary absorbing set is obtained. Lastly, by using sobolev compact embedding and contraction function,the asymptotic compactness of semigroups is proved. Thus, we get the existence of global attractor of the system.

关 键 词：记忆项 非局部板方程 整体吸引子 

分 类 号：O175.29[理学—数学]