Communications in Mathematical Sciences

Volume 2 (2004)

Number 2

Burgers' Equation with Vanishing Hyper-Viscosity

Pages: 317 – 324

(Fast Communication)



Eitan Tadmor


We prove that bounded solutions of the vanishing hyper-viscosity equation, converge to the entropy solution of the corresponding convex conservation law. The hyper-viscosity case 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.

Full Text (PDF format)