Macroscopic boundary conditions on a solid surface in rarefied gas flow for a one-dimensional nonlinear nonstationary 12-moment system of Boltzmann equations

Boundary conditions for a one-dimensional nonlinear nonstationary system of Boltzmann equations are formulated in the fifth approximation. The Maxwell microscopic boundary conditions are approximated in the case of the one-dimensional Boltzmann equation when some of the molecules reflect specularly from the surface, while the others reflect diffusely with Maxwell's distribution. An initial-boundary value problem for the 12-moment system of Boltzmann equations with Maxwell–Auzhani boundary conditions is stated. For the 12-moment system of Boltzmann equations, six boundary conditions are set at the left and right endpoints of the interval ($-a$, $a$ ).