Analytic solution of the nonhomogeneous linear kinetic equation in the heat slip flow problem

An analytic method for solving the model Boltzmann nonhomogeneous equation with BGK collision operator is presented. The equation reduces by separate variables to the characteristic equation, for which in space of generalized function the eigenfunctions and the eigenvalues are found. The expansion of the distribution function for the boundary value problem by the eigenfunctions is proved. The expansions of the solution of this problem are expansions by singular Fourier integrals.