BURGERS’ EQUATION WITH VANISHING HYPER-VISCOSITY*

Abstract

We prove that bounded solutions of the vanishing hyper-viscosity equation, (Formula Presented) converge to the entropy solution of the corresponding convex conservation law (Formula Presented). The hyper-viscosity case, s > 1, lacks the monotonicity which underlines the Krushkov BV theory in the viscous case s = 1. Instead we show how to adapt the Tartar-Murat compensated compactness theory together with a weaker entropy dissipation bound to conclude the convergence of the vanishing hyper-viscosity.