Asymptotic methods in the theory of linear kinetic equations

For the example of the Fokker–Planck equation with arbitrary coefficients, asymptotic (with respect to the time) solutions of linear kinetic equations are constructed by means of the formalism of Green's functions as well as by the method of quasistationary distribution functions. An expression is obtained for the eigenvalue of minimal absolute magnitude and the corresponding eigenfunction. An algorithm is given for calculating the following eigenvalues. Over a finite interval, the asymptotic solutions found for the Fokker–Planck equation coincide. The method of quasistationary distribution functions is more general than the methods using eigenvalues and eigenfunctions.