Forward-backward parabolic equations

We study the forward-backward problems which arise in many applications in physical and biological phenomena. Since the forward-backward problems are in general ill-posed, we investiagte their regularized problems which are expected to be well-posed. By the different physical meaning of the regularized terms, we obtain the different solutions of the original problems. In our work, we address the Sobolev regularization and Cahn-Hilliard regularization.The European Community's Seventh Framework Programme (FP7/2007-2013) and University of Rome La Sapienza