| 一类耗散动力系统的有限维约化 |
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| 引用本文： | 崔振琼,杨成明,王荣年.一类耗散动力系统的有限维约化[J].上海师范大学学报(自然科学版),2022,51(3):257-262. |
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| 作者姓名： | 崔振琼 杨成明 王荣年 |
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| 作者单位： | 上海师范大学 数理学院, 上海 200234 |
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| 基金项目： | 国家自然科学基金(11971317,11471083) |
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| 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.
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| 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 |
| 收稿时间： | 2022/4/20 0:00:00 |
Finite-dimensional reduction of a class of dissipative dynamical systems |
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| CUI Zhenqiong,YANG Chengming,WANG Rongnian.Finite-dimensional reduction of a class of dissipative dynamical systems[J].Journal of Shanghai Normal University(Natural Sciences),2022,51(3):257-262. |
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| Authors: | CUI Zhenqiong YANG Chengming WANG Rongnian |
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| Institution: | Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China |
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| 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. |
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| Keywords: | coupled system of semilinear evolution equations infinite-dimensional dynamical system finite-dimensional invariant manifold reduction |
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