Local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping Original Research Article

We consider the wave equation with interior and boundary nonlinear sources and damping and we are interested in local and global wellposedness of finite energy solutions. The main difficulty is represented by the fact that the Lopatinski condition fails to hold (unless the dim(Ω)=1dim(Ω)=1), and thus the analysis of the boundary nonlinearities becomes a subtle issue.