Communications in Mathematical Sciences
- Commun. Math. Sci.
- Volume 2, Number 2 (2004), 317-324.
Burgers' Equation with Vanishing Hyper-Viscosity
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.
Commun. Math. Sci., Volume 2, Number 2 (2004), 317-324.
First available in Project Euclid: 1 March 2005
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Tadmor, Eitan. Burgers' Equation with Vanishing Hyper-Viscosity. Commun. Math. Sci. 2 (2004), no. 2, 317--324. https://projecteuclid.org/euclid.cms/1109706540