Invariant Manifolds Of Semi-linear Hyperbolic-parabolic Coupled Equations

We investigate the existence of invariant manifolds for a coupled problem of nonlinear hyperbolic-parabolic PDEs in 3-D torus.The problem arises usually in the study of wave propagation phenomena with viscous damping which are heat generating.The spectral gap condition already fails for it.We prove that the dynamical system determined by it possesses a Lipschitz manifold which is locally invariant under the semiflow.The locally asymptotic stability and regularity of the manifold are also considered.Moreover,under more assump-tions,it is proved that the manifold is provided with the feature as that global manifold usually holds.Through it all,no large damping and heat diffusivity are needed.