Viscous Shock Motion for Advection‐Diffusion Equations

Abstract

This paper studies the asymptotic solution of the initial‐boundary value problem for scalar convection‐dominated evolution equations on a bounded spatial domain when initial and boundary conditions are such that the solution develops a single thin shock layer of steep change. The exponentially slow motion of the shock is determined for exponentially long times using an ansatz based on the solution for the special case of Burgers' equation, obtained through the Cole‐Hopf transformation. Results obtained analytically are confirmed by numerical experiments.