摘要
考虑带有记忆的Boussinesq方程解的长时间动力学行为.首先通过引入新的变量将原方程转化为一个动力系统,然后利用算子分解技巧及历史空间上的紧性定理证明所研究问题对应解半群的紧性;最后结合指数吸引子的存在性得到记忆型Boussinesq方程的指数吸引子,从而获得了该问题全局吸引子的有限分形维数.
We considered the long-time dynamical behavior of solutions of Boussinesq equations with memory.Firstly,the original equation was transformed into a dynamical system by introducing a new variable.Secondly,the compactness of corresponding solutions semigroups associated with problem was proved by using the technique of operator decomposition and the compactness theorem on historical spaces.Finally,the exponential attractor of the memory-type Boussinesq equation was obtained by combining the existence of the exponential attractor,and the finite fractal dimension of the global attractor of the problem was obtained.
作者
王美霞
马巧珍
WANG Meixia;MA Qiaozhen(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)
出处
《吉林大学学报（理学版）》
CAS
北大核心
2019年第6期1319-1332,共14页
Journal of Jilin University:Science Edition
基金
国家自然科学基金(批准号:11561064)
西北师范大学创新团队基金(批准号:NWNU-LKQN-14-6)
