A Shock Layer in Parabolic Perturbations of a Scalar Conservation Law

Abstract

A definition of a shock layer of thickness δ is proposed when a parabolic perturbation is applied to a scalar conservation law. The asymptotic equality δ √ ε is established, where ε denotes viscosity. This equality is proved to be optimal. Nevertheless, the equality δ ε is also proved to be valid for a class of shocks in accordance with the Mises conjecture.