Variational Principles for Propagation Speeds in Inhomogeneous Media

Abstract

An important problem in reactive flows is how to estimate the speed of front propagation, especially when inhomogeneities are present. Here we prove a variational characterization of the front speed for reaction-diffusion-advectionequations in periodically varying heterogeneous media. This formulation makes it possible to calculate sharp estimates for the speed explicitly. The method can be applied to any problem obeying a maximum principle. Three examples will be analyzed in detail: a shear flow problem, a problem with rapidly oscillating coefficients, and a discretized diffusion problem. In all cases the effects of the inhomogeneous medium on the speed are discussed in comparison to the homogeneous problem. For the shear flow problem, enhancement of the speed results.