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一类耗散动力系统的有限维约化
崔振琼, 杨成明, 王荣年
上海师范大学 数理学院, 上海 200234
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.
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
DOI:10.3969/J.ISSN.1000-5137.2022.03.001
分类号:O192
基金项目:国家自然科学基金(11971317,11471083)
Finite-dimensional reduction of a class of dissipative dynamical systems
CUI Zhenqiong, YANG Chengming, WANG Rongnian
Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
Abstract:
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.
Key words:  coupled system of semilinear evolution equations  infinite-dimensional dynamical system  finite-dimensional invariant manifold  reduction