Gradient-like dynamics: motion near a manifold of quasi-equilibria

CDSNS Colloquium
Monday, September 24, 2018 - 11:15am
1 hour (actually 50 minutes)
Skiles 005
Michigan State University
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.