Title: Kawashima condition for a hyperbolic moment model of phonon hydrodynamics

Authors: Zbigniew Banach, Wieslaw Larecki

Addresses: Institute of Fundamental Technological Research, Department of Theory of Continuous Media, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland. ' Institute of Fundamental Technological Research, Department of Theory of Continuous Media, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland

Abstract: We consider a 3 × 3 hyperbolic symmetrisable phonon system of balance laws that describes the one-dimensional flow evolution of the energy density, the heat flux and the flux of the heat flux. This system possesses a strictly concave homogeneous entropy function and is derived by taking moments of the reduced Boltzmann-Peierls equation with Callaway|s collisional term and subsequently truncating and closing the resulting moment equations by means of the entropic approximation. Employing the entropy dissipation condition and the Kawashima condition, we verify the existence of global smooth solutions for initial data close enough to a constant equilibrium state. The two formulations are used: the formulation in terms of the entropy variables and the formulation in terms of the primitive variables.

Keywords: phonon hydrodynamics; symmetrisable hyperbolic systems; strictly concave entropy; global smooth solutions; Kawashima condition; hyperbolic moment model; flow evolution; energy density; heat flux.

DOI: 10.1504/IJDSDE.2008.023003

International Journal of Dynamical Systems and Differential Equations, 2008 Vol.1 No.4, pp.263 - 275

Published online: 06 Feb 2009 *

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