Wave equations with super-critical interior and boundary nonlinearities

This article presents a unified overview of the latest, to date, results on boundary value problems for wave equations with super-critical nonlinear sources on both   the interior and the boundary of a bounded domain Ω∈Rn. The presented theorems include Hadamard local wellposedness, global existence, blow-up and non-existence theorems, as well as estimates on the uniform energy dissipation rates for the appropriate classes of solutions.