The bimodal approximate solution of the Boltzmann equation in the sence of distributions

An approximation of the solution of the nonlinear three-dimensional Boltzmann equation for hard spheres in the sence of distributions is proposed. The approximate solution is built as a spatially-nonhomogeneous nonstationary linear combination of two $\delta$-functions on velocity, which are concentrated at different points. It is shown that the error between the left and the right sides of the equation may be reduced to arbitrary small values when parameters, involved in distribution, tend to their limit values, in particular, when the mass velocities at $+\infty$ and $-\infty$ are different but the Knudsen number is quite large.