具有温和阻尼的非线性热弹耦合系统的整体吸引子

Global Attractor for the Nonlinear of Thermoeasticl Coupled System with Gentle Dissipation

本文研究有界区域下带有温和阻尼的非线性热弹耦合系统的整体解的适定性和整体吸引子的问题.首先,利用Faedo-Galerkin的方法,证明初边值问题弱解的适定性,其次根据解的适定性构造了动力系统,最后给出系统有界吸收集的存在性和半群的一致紧性,证明了系统整体吸引子的存在性.

In this paper,the problem of the well-posedness of global solution and global attractor for nonlinear thermoelastic coupled systems with gentle dissipation in bounded regions are studied.Firstly,the adaptability of the weak solution of the initial boundary value problem is proved by using the Faedo-Galerkin method.Secondly,the dynamic system is constructed according to the adaptability of the solution.Finally,the existence of the bounded absorption set and the uniform compactness of the semigroup are given,and the existence of the global attractor of the system is proved.