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 $\Omega \in {‐R}^n$ . 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.