A Finite-dimensional Invariant Manifold For A Class Of Thermoelastic Models

We study finite-dimensional invariant manifolds for the following model of thermoe-lasticity(?) The model consists of a weakly damped wave equation and a heat equation.It arises in the study of string vibration phenomenon.This dissertation consider homogeneous Dirich-let boundary conditions.We first establish a general framework and obtain an abstract invariant manifold theorem,by means of the Lyapunov-Perron method.In the sequel,it is proved,using this theorem,that when the dissipation parameters ?,d are suitably large,the dynamical system,generated by the model,possesses a finite-dimensional Lipschitz manifold.This manifold is locally invariant and exponentially attracting,which contain-s the global attractor.The proofs of above results are based on the following fact:the second-order partial differential operator(?)has arbitrarily large spectral gaps.