Abstract
We present a one-dimensional non-stationary nonlinear moment system of equations and an approximation of the microscopic boundary condition when part of the molecules is reflected from the surface specularly and part is diffuse with the Maxwell distribution. The system of moment equations and the macroscopic boundary conditions depend on the flight speed and the surface temperature of the aircraft. The system of moment equations represent nonlinear hyperbolic system of equations. We prove correctness of the initial and boundary value problem for the system of moment equations in the third approximations under the macroscopic boundary conditions.