Communications in Mathematical Sciences

Burgers' Equation with Vanishing Hyper-Viscosity

Eitan Tadmor

Abstract

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.

Article information

Source
Commun. Math. Sci., Volume 2, Number 2 (2004), 317-324.

Dates
First available in Project Euclid: 1 March 2005

Permanent link to this document
https://projecteuclid.org/euclid.cms/1109706540

Mathematical Reviews number (MathSciNet)
MR2119943

Zentralblatt MATH identifier
1088.35038

Citation

Tadmor, Eitan. Burgers' Equation with Vanishing Hyper-Viscosity. Commun. Math. Sci. 2 (2004), no. 2, 317--324. https://projecteuclid.org/euclid.cms/1109706540


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