Kawashima condition for a hyperbolic moment model of phonon hydrodynamics
by Zbigniew Banach, Wieslaw Larecki
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 1, No. 4, 2008

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.

Online publication date: Fri, 06-Feb-2009

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