This award will provide support for Juan Redondo, who is a postdoc at the University of Michigan working with Professor Jeff Rauch. Dr. Redondo plans to continue his study of the regularity of free boundaries in the solutions of parabolic variational inequalities like the ones associated with the classical Stefan problem. He is also going to investigate the regularity of shock wave solutions of hyperbolic conservation laws by applying his variational techniques to the parabolic systems that come from adding viscous terms to the original hyperbolic systems. Nonlinear partial differential equations describe many dissipative phenomena like the flow of heat. If the amount of dissipation is small the solutions of such equations often behave as if there is no dissipation at all. In this grant the postdoc, Juan Redondo, will use techniques from variational theory that exploit this relationship between dissipative and non-dissipative systems in order to study things like the shape of a boundary between different materials and the sharpness of a front between gases of different densities.
