Speed selection for reaction diffusion equations in heterogeneous environments

Abstract

Reaction-advection-diffusion equations, in periodic settings and with general type nonlinearities, admit a threshold known as the minimal speed of propagation. The minimal speed does not have an accessible formula when the nonlinearity is not of KPP type, for instance. The question becomes whether the minimal speed can be obtained through a linearization procedure or not. In this paper, we derive selection criteria for the minimal speed: a key feature of the nonlinear selection is unveiled. Moreover, we use upper/lower solution techniques in order to derive practical criteria determining the minimal speed in the presence of advection and a general type nonlinearity.