Nonstationary boundary problem for model kinetic equations at critical parameters

Nonstationary solutions of the model kinetic equation at critical values of the motion of the wall (the boundary of the half-space occupied by gas) are studied. The characteristic equation is obtained by separating the variables. The eigenfunctions and the eigenvalue spectrum are found in the distribution space. A solution to the equation is expandable over the eigenfunction basis. The Rayleigh problem is considered as an application. The distribution function is continuous in the plane of the wall-motion parameters, including the closed curve of critical parameter values.