时变时滞粘弹性板方程的整体吸引子  

Global Attractor for a Viscoelastic Plate Equation with Time-Varying Delay

作　　者：卢瑞涵 任永华 LU Ruihan;REN Yonghua(College of Mathematics,Taiyuan University of Technology,Jinzhong 030600,China)

机构地区：[1]太原理工大学数学学院,山西晋中030600

出　　处：《应用数学》2020年第2期263-274,共12页Mathematica Applicata

基　　金：国家自然科学基金(11872264)。

摘　　要：本文研究内部反馈中具有历史和时变时滞的粘弹性板方程.首先利用Faedo-Galerkin方法证得方程在初边值条件下解的适定性定理;其次通过构造合适的能量泛函和Lyapunov泛函证明系统的梯度性;最后利用乘子泛函建立稳定不等式,证明系统的拟稳定性及渐近光滑性,从而得到整体吸引子的存在性,并证明了该吸引子具有有限分形维数.In this paper,the viscoelastic plate equation with past history and time-varying delay in the internal feedback is studied.Firstly,the Faedo-Galerkin method is used to prove the well-posedness of the solution under the initial-boundary value condition,and then the gradient property of the system is proved by constructing appropriate energy functional and Lyapunov functional.Finally,a stable inequality is established by using the multiplier functional to prove the quasi-stability and asymptotic smoothness of the system,thus the existence of the global attractor is obtained,and the finite fractal dimension of the attractor is proved.

关 键 词：板方程 粘弹性 时变时滞 整体吸引子 有限分形维数 

分 类 号：O175.29[理学—数学]