强阻尼波方程全局吸引子的存在性  

The existence of global attractors for damped wave equation

作　　者：王会超 李军燕[2] WANG Hui-chao;LI Jun-yan(School of Science,Xuchang University,Xuchang 461000,Henan,China;Jincheng College of Sichuan University,Chengdu 611731,Sichuan,China)

机构地区：[1]许昌学院数理学院,河南许昌461000 [2]四川大学锦城学院,四川成都611731

出　　处：《西北师范大学学报（自然科学版）》2020年第6期6-10,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11701399)。

摘　　要：运用标准的Galerkin方法证明了一类带阻尼项波方程全局弱解的存在性,在此基础上建立了强连续算子半群;在一定的假设条件下,得到了半群有界吸收集的存在性,进而借助C-条件方法证明了方程具有全局吸引子.By using the standard Galerkin method,the existence of global weak solution for damped wave equation is obtained in this paper.Then on this basis,the strong continuously operator semigroup is set up.With certain assumption,the bounded absorbing set for the continuously semigroup is obtained.Finally,the existence of global attractors for damped wave equation is proved by using C-condition method.

关 键 词：全局弱解 C-条件 算子半群 吸收集 全局吸引子 

分 类 号：O175.2[理学—数学]