Regular asymptotic expansion of the linearized Bhatnagar-Gross-Krook equation

The dissipative relaxation of a plane acoustic wave in a quiescent homogeneous gas is studied with the linearized Bhatnagar-Gross-Krook equation. For small Knudsen numbers, a solution is constructed with the multiscale expansion technique. A self-consistent solution uniformly applicable in the large-time limit is extended to the fourth super-Barnett approximation. Expressions for the parameters of the wave, including Knudsen corrections to the damping rate, are derived. A value of the solutions obtained in this paper is that they make it possible to estimate the validity of assumptions.