Abstract
The reformulation of conservation laws in terms of kinetic equations, which parallels the relation between Boltzmann and Euler equation, has been successfully used in the form of kinetic schemes. The central problem in the kinetic approach is the construction of suitable equilibrium distributions which generalize the Maxwellian in the Boltzmann—Euler case. Here, we present a solution to this problem which allows the construction of equilibrium distributions for general systems of hyperbolic conservation laws. The approach leads to the notion of higher order entropies and generalizes several approaches discussed by other authors.
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Junk, M. (2001). A Kinetic Approach to Hyperbolic Systems And the Role of Higher Order Entropies. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. ISNM International Series of Numerical Mathematics, vol 141. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8372-6_12
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DOI: https://doi.org/10.1007/978-3-0348-8372-6_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9538-5
Online ISBN: 978-3-0348-8372-6
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