Exact linearization of the sliding problem for a dilute gas in the Bhatnagar–Gross–Krook model

We consider the nonlinear Boltzmann equation in the Bhathnagar–Gross–Krook model for the gas flow in a half-space (the Kramers problem). The problem can be exactly linearized, and its solution can be reduced to a linear integral equation with an addition–difference kernel and a simple nonlinear relation.