Existence and uniqueness of propagating terraces

Abstract

This work focuses on dynamics arising from reaction-diffusion equations, where the profile of propagation is no longer characterized by a single front, but by a layer of several fronts which we call a propagating terrace. This means, intuitively, that transition from one equilibrium to another may occur in several steps, that is, successive phases between some intermediate stationary states. We establish a number of properties on such propagating terraces in a one-dimensional periodic environment under very wide and generic conditions. We are especially concerned with their existence, uniqueness, and their spatial structure. Our goal is to provide insight into the intricate dynamics arising from multistable nonlinearities.