| 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) |
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| Finite-dimensional reduction of a class of dissipative dynamical systems |
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CUI Zhenqiong, YANG Chengming, WANG Rongnian
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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. |
| Key words: coupled system of semilinear evolution equations infinite-dimensional dynamical system finite-dimensional invariant manifold reduction |
