Lorena Bociu (University of Nebraska)
Title: Supercritical Sources in Nonlinear Wave Equations
Abstract: The model under consideration is the semilinear wave equation with supercritical nonlinear sources and damping terms and our aim is to discuss the wellposedness of the system on finite energy space. A distinct feature of the equation is the presence of the double interaction of source and damping, both in the interior of the domain and on the boundary. Moreover, the nonlinear boundary sources are driven by Neumann boundary conditions. Since Lopatinski condition fails to hold for dimension greater or equal than 2, the analysis of the nonlinearities supported on the boundary, within the framework of weak solutions, is a rather subtle issue and involves strong interaction between the source and the damping. I will provide positive answers to the questions of local existence and uniqueness of weak solutions and moreover give complete and sharp description of parameters corresponding to global existence and blow-up of solutions in finite time.