A criterium of smallest of the difference for bimodal solution of the Boltzmann equation

For an explicit approximate solution of the Boltzmann equation in the form of a spatially-inhomogeneous linear combination of two Maxwellians with different mass velocities an exact low-temperature asymptotic of the difference between the left and right sides of the equation in the sense of integral metric is calculated. Necessary and sufficient conditions of tending of this difference to zero are derived by choosing values of parameters entering into the solution.