Christopher Jones, University of North Carolina at Chapel Hill

Stability of Equilibria of Reaction-Diffusion Equations and the Morse Index Theorem

Abstract:  For scalar reaction-diffusion equations in one space dimension, the stability of equilibria, and traveling waves can be determined by Sturm-Liouville theory. The Morse Index Theorem for geodesics on a Riemannian manifold can be viewed as a generalization of Sturm-Liouville theory to systems of equations, but still in one space dimension. This can also be applied to systems of PDEs that arise in applications if they have a certain gradient structure. The question addressed will concern how to extend these dynamical systems based ideas to multi-dimensional domains.

Address: Applied Mathematics, CB #3250 Phillips Hall University of North Carolina at Chapel Hill Chapel Hill, NC  27599-3250.

                http://www.amath.unc.edu/Faculty/ckrtj/