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We consider two classes of linear kinetic equations: with constant collisionfrequency and constant mean free path of gas molecules (i.e., frequency ofmolecular collisions, proportional to the modulus molecular velocity). Basedhomogeneous Riemann boundary value problem with a coefficient equal to theratio of the boundary values dispersion function, develops the theory of thehalf-space orthogonality of generalized singular eigenfunctions correspondingcharacteristic equations, which leads separation of variables. And in this twoboundary value problems of the kinetic theory (diffusion light component of abinary gas and Kramers problem about isothermal slip) shows the application ofthe theory orthogonality eigenfunctions for analytical solutions these tasks.

Theory of orthogonality of eigenfunctions of the characteristic equations as a method of solution boundary problems for model kinetic equations