Almost Planar Waves in Anisotropic Media

Abstract

We investigate corners and steps of interfaces in anisotropic systems. Starting from a stable planar front in a general reaction-diffusion-convection system, we show existence of almost planar interior and exterior corners. When the interface propagation is unstable in some directions, we show that small steps in the interface may persist. Our assumptions are based on physical properties of interfaces such as linear and nonlinear dispersion, rather than properties of the modeling equations such as variational or comparison principles. We also give geometric criteria based on the Cahn–Hoffman vector, that distinguish between the formation of interior and exterior corners.