Fronts Between Periodic Patterns for Bistable Recursions on Lattices

Tuesday, December 4, 2012 - 2:00pm - 2:50pm
Keller 3-180
Bastien Fernandez (Centre National de la Recherche Scientifique (CNRS))
Bistable space-time discrete systems commonly possess a large variety of stable stationary solutions with
periodic profile. In this context, it is natural to ask about the fate of trajectories composed of interfaces
between steady configurations with periodic pattern and in particular, to study their propagation as
traveling fronts. In this talk, I will consider such fronts in piecewise affine bistable recursions on the one-dimensional lattice. By introducing a definition inspired by symbolic dynamics, I will present results on
the existence of front solutions and the uniqueness of their velocity, upon existence of their ground patterns. Moreover, the velocity dependence on parameters and the co-existence of several fronts with
distinct ground patterns will also be described. Finally, robustness of the results to small C1-perturbations of the piecewise affine map will be argued by mean of continuation arguments.
MSC Code: