A Finite-dimensional Reduction Of A Class Of Dissipative Dynamical Systems

The dissertation is concerned with a class of coupled system of semilinear evolution equations defined on infinite-dimensional 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(which is also called a reduced system)and clarify the relationship of attractor and equilibrium between the original system and the reduced system.