Special Session 14: New perspectives in the qualitative study of nonlinear differential equations and dynamical systems

Propagating terraces in periodic media
Thomas Giletti
University Clermont-Auvergne
France
Co-Author(s):    Luca Rossi
Abstract:
In this talk, we will be interested in the propagation of solutions of a multistable reaction-diffusion equation in spatially periodic media. We will prove the existence of a so-called propagating terrace, which is a finite sequence of fronts whose speeds are ordered. These correspond to a situation where successive transitions occur between intermediate steady states. We will see that propagating terraces dictate the large-time behavior of solutions of the Cauchy problem, but also that new difficulties arise from the interplay between the different directions of propagation.