Longtime Behaviour of Strongly Damped Wave Equations, Global Attractors and Their Dimension

This paper contains some results on asymptotic behaviour of solutions to strongly damped abstract nonlinear wave equations. After reviewing sufficient hypotheses for existence and uniqueness, uniform time estimates are given and a global attractor for the trajectories of the associated dynamical system is constructed. Finally, applications are made to nonlinear wave equations such as Sine–Gordon equation, proving the finite dimensionality of the corresponding attractors.