一类具有非线性kirchhoff-sine-Gordon广义方程的整体吸引子的存在性  

Global Attractor for a Class of Nonlinear Generalized kirchhoff-sine-Gordon Equation

作　　者：姚华珍 张建文 YAO Hua-zhen;ZHANG Jian-wen(Taiyuan University of Technology,College of Mechanical and Vehicle Engineering,Taiyuan 030024,China;Taiyuan University of Technology,College of Mathematics,Taiyuan 030024,China)

机构地区：[1]太原理工大学机械与运载工程学院,山西太原0300241 [2]太原理工大学数学学院,山西太原030024

出　　处：《数学的实践与认识》2020年第8期208-215,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11872264)。

摘　　要：主要目的是利用Galerkin逼近法和先验估计来证明一类具有非线性阻尼和外源项的耗散型sine-Gordon-kirchhoff方程的整体吸引子的存在性,首先通过先验估计证明系统存在唯一的整体解,再证明系统存在有界吸收集和算子半群光滑性质,最后得到系统存在整体吸引子.The aim of this paper is to prove the existence and uniqueness of the global attractor for the dissipative sine-Gordon-kirchhoff type equation with nonlinear damping and source terms on R^n,by using the Galerkin approximation method and priori estimates.Firstly,the existence and uniqueness of global solution of the system are proved by a priori estimate,and then the existence of bounded absorption set and smoothness of operator semigroup is proved.Finally,the existence of global attractor of the system is obtained.

关 键 词：整体吸引子 先验估计 kirchhoff-sine-Gordon方程 非线性阻尼 

分 类 号：O175.29[理学—数学]