Abstract
A one-dimensional nonstationary nonlinear moment system of equations and an approximation of Maxwell’s microscopic boundary condition will be introduced. The flight speed and surface temperature of the aircraft are included in the moment system of equations as coefficients. Macroscopic boundary conditions also depend on the surface temperature of the aircraft. The quantity of macroscopic boundary conditions for the moment system of equations depends on the parity of the approximation number of the moment system of equations. We state the initial and boundary value problem for the moment system of equations in the third approximation under macroscopic boundary conditions. This paper proves the existence and uniqueness of the solution of the abovementioned problem in the space of functions continuous in time and summable in the square by spatial variable. The theorem on the existence and uniqueness of a solution of the initial and boundary value problem for the moment system of equations in the third approximation is proved by the method of a priori estimation and using the Galerkin method and Tartar’s compensated compactness method.