Relaxation of the distribution function tails for gases with power-law interaction potentials

The relaxation of rarefied gases of particles with the power-law interaction potentials U=α/rˢ, where $1<~s<4,$ is considered. The formation and evolution of the distribution function tails are investigated on the basis of the one-dimensional kinetic Landau--Fokker-Planck equation. For long times, the constructed asymptotic solutions have a propagating-wave appearance in the high velocity region. The analytical solutions are expressed explicitly in terms of the error function. The analytical consideration is accomplished by numerical calculations. The obtained analytical results are in a good agreement with the numerical simulation results.