Long-term analysis of strongly damped nonlinear wave equations

We consider the strongly damped nonlinear wave equation u_tt − Delta u_t − Delta u + f (u_t ) + g(u) = h with Dirichlet boundary conditions, which serves as a model in the description of thermal evolution within the theory of type III heat conduction. In particular, the nonlinearity f acting on u_t is allowed to be nonmonotone and to exhibit a critical growth of polynomial order 5. The main focus is the long-term analysis of the related solution semigroup, which is shown to possess the global attractor in the natural weak energy space.