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A SHOCK LAYER IN PARABOLIC PERTURBATIONS OF A SCALAR CONSERVATION LAW

Published online by Cambridge University Press:  04 July 2003

Vladimir Shelukhin
Vladimir Shelukhin
Affiliation:
Lavrentyev Institute of Hydrodynamics, Novosibirsk, 630090, Russia (shelukhin@hydro.nsc.ru)
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Abstract

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A definition of a shock layer of thickness $\delta$ is proposed when a parabolic perturbation is applied to a scalar conservation law. The asymptotic equality $\delta\asymp\sqrt{\varepsilon}$ is established, where $\varepsilon$ denotes viscosity. This equality is proved to be optimal. Nevertheless, the equality $\delta\asymp\varepsilon$ is also proved to be valid for a class of shocks in accordance with the Mises conjecture.

AMS 2000 Mathematics subject classification: Primary 35L67. Secondary 35K65

Keywords

Riemann problemshockparabolic perturbation

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 2 , June 2003 , pp. 315 - 328
Copyright
Copyright © Edinburgh Mathematical Society 2003