Strongly damped wave equations with critical nonlinearities

Abstract

This note deals with the strongly damped nonlinear wave equation utt−Δut−Δu+f(ut)+g(u)=h with Dirichlet boundary conditions, where both the nonlinearities f and g exhibit a critical growth, while h is a time-independent forcing term. The existence of an exponential attractor of optimal regularity is proven. As a corollary, a regular global attractor of finite fractal dimension is obtained.