On One Nonlinear Boundary-Value Problem in Kinetic Theory of Gases

In the paper, the solvability of one nonlinear boundary-value problem arising in kinetic theory of gases is studied. We prove the existence of global solvability of a boundary-value problem in the Sobolev space $W_{\infty}^1(\mathbb{R}^+).$ The limit of the solution is found by using some a'priori estimations. For the case of power nonlinearity, the uniqueness of the solution in a certain class of functions is proved. Some examples illustrating the obtained results are given.