Abstract:

We discuss recent progress on one-dimensional interface models in the
presence of strong scale separation. Here the interplay of dynamical
systems theory and parabolic PDE can be made surprisingly explicit. We
combine geometric singular perturbation theory, the Evans-function for
stability analysis, center manifold reduction, normal form and
singularity theory. This allows to detect and unfold degenerate
Takens-Bodganov points for the interface dynamics, which features
various periodic, homoclinic and heteroclinic solutions. The results are
illustrated with numerical computations.