一类耗散动力系统的有限维约化

Finite-dimensional reduction of a class of dissipative dynamical systems

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.