一类耗散动力系统的有限维约化  

Finite-dimensional reduction of a class of dissipative dynamical systems

作　　者：崔振琼 杨成明 王荣年 CUI Zhenqiong;YANG Chengming;WANG Rongnian(Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2022年第3期257-262,共6页Journal of Shanghai Normal University(Natural Sciences)

基　　金：国家自然科学基金(11971317,11471083)。

摘　　要：考虑一类定义在无限维Banach空间上的半线性耦合发展方程组.利用方程组生成无限维动力系统的一个有限维不变流形,研究有限维约化问题.更详细地,利用有限维不变流形得到一个有限维系统(称之为约化系统),并澄清了原系统和约化系统之间吸引子和平衡解的关系.The paper considers a class of coupled system of semilinear evolution equations defined on infinitedimensional Banach spaces.A finite-dimensional invariant manifold of infinite-dimensional dynamical system generated by the coupled system can be used to derive a reduction principle.More precisely,making use of the invariant manifold,we can obtain a finite-dimensional system(also called a reduced system),and clarify the connection of attractor and equilibrium between the original system and the reduced system.

关 键 词：半线性耦合发展方程组 无限维动力系统 有限维不变流形 约化 

分 类 号：O192[理学—数学]