Derivation of Hyperbolic Transfer Equations from BGK-Equation

摘要

We use the integral form of the Boltzmann equation which allows us to takeinto account the memory effects using the initial condition that selects thesolutions going to the local equilibrium Maxwell distribution in the $t \to-\infty$ limit. Implementing the relaxation-time approximation for thecollision integral (BGK-equation) we present the derivation of the hyperbolicNavier-Stokes and the hyperbolic heat conduction equations in the first orderapproximation. It is shown that the relaxation time in the obtained hyperbolicequations is the Maxwellian relaxation time. As special case we obtain thetelegraph equation for the heat propagation in static medium and estimate therelaxation time for the heat conduction in some materials.