Evolution of a Two-Dimensional Moving Contrast Structure in an Inhomogeneous Medium with Advection

Abstract

We consider the problem of evolution of the internal transition layer for two-dimensional quasilinear initial-boundary value problem for the reaction-advection-diffusion equation in an inhomogeneous medium with a small parameter for higher derivatives. It is shown that in the zero (principal) order of the asymptotic series, the position of the internal transition layer is described by the Hamilton–Jacobi equation. The potential is calculated as an integral of the source density function within the limits of the equilibrium levels. The front line of the transition layer evolves in the same way as the constant-eikonal line (or wavefront line) for the problem of wave propagation in an inhomogeneous medium in short-wave (geometro-optical) asymptotics. The sum of the zero-and first-order asymptotic series is found. The destruction time of the contrast structure is evaluated.