May 20, 2014 – Alberto Tesei, University of Rome I

Title : Pseudo-Parabolic Regularization of Forward-Backward Parabolic Equations

It is known that, depending on the behaviour at infinity of the response function,
solutions of forward-backward parabolic equations can develop singularities as time evolves (e.g., this is the case for the Peron-Malik equation). To address these phenomena Radon measure-valued solutions must be considered. We discuss some recent results (obtained jointly with M. Bertsch and F. Smarrazzo) concerning existence of such solutions, as well as dependence of their qualitative properties on different regularizations.