Damped wave equations with fast growing dissipative nonlinearities (Q833270)

Dirichlet initial-boundary value problem to the equation \(u_{tt}+au_t -\Delta u=f(u)\) in \((0,\infty)\times \Omega\), where \(a>0\) and \(\Omega\) is a bounded smooth domain in \(\mathbb R^n\) (\(n\geq 3\)), is considered. The authors construct global weak solutions of the problems as limits of solutions to the equations involving a strong damping term. They prove existence of a compact attractor to these solutions. Under an additional assumption uniqueness of the solution for \(n=3,4,5\) is proved.