This concerns general gradient-like dynamical systems in Banach space with the property that there is a manifold along which solutions move slowly compared to attraction in the transverse direction. Conditions are given on the energy (or, more generally, Lyapunov functional) that ensure solutions starting near the manifold stay near for a long time or even forever. Applications are given with the vector Allen-Cahn and Cahn-Morral equations. This is joint work with Giorgio Fusco and Georgia Karali.
Peter Bates is a Professor at Michigan State University, having served as Chair of the Mathematics Department before returning to teaching and research. Prior to MSU he held a professorship in Mathematics at Brigham Young University, where he also served for some time as the Chairperson of the Mathematics Department and the Director of the Nonlinear Analysis Lab. Before that he held an Associate Professorship at Texas A&M University. For two years he was the Director of the Applied Mathematics Program at the National Science Foundation in Washington DC. His interests include nonlinear PDEs and infinite-dimensional dynamical systems and applications to materials science and mathematical biology. Some of his recent work includes invariant manifold theory and geometric singular perturbation theory for stochastic dynamical systems.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai