On the convergence of attractors and exponential attractors for singularly perturbed hyperbolic equations

This paper studies the dynamical behavior of parabolic equations under singular hyperbolic perturbations. In particular it is shown that for damped semilinear hyperbolic equations that are obtained as a singular perturbation of a parabolic equation, a finite dimensional global attractor exists and as the perturbation parameter tends to zero the attractor of the hyperbolic equation converges in some sense to the attractor of the corresponding parabolic partial differential equation. As the most challenging example, the authors treat throughout the paper the case of Klein-Gordon equation in three dimensional space when damping, which is inversely related to the perturbation parameter, is very large. (Authors)