The one-dimensional kinetic equation with integral of collisions type BGK (Bhatnagar, Gross and Krook) and frequency of collisions affine depending on the module of molecular velocity is constructed.Laws of preservation of number of particles, momentum and energy at construction equation are used.Separation of variables leads to the characteristic equation. The system of the dispersion equations is entered. Its determinant is called as dispersion function. It is investigated continuous and discrete spectra of the characteristic equation.The set of zero of the dispersion equation makes the discrete spectrum of the characteristic equation. The eigen solutions of the kinetic equation corresponding to discrete spectrum are found.The solution of the characteristic equation in space of the generalized functions leads to eigen functions corresponding to the continuous spectrum.Results of the spent analysis in the form of the theorem about structure of the general solution of the entered kinetic equation are formulated.

For the one-dimensional linear kinetic equation analytical solutions of problems about temperature jump and weak evaporation (condensation) over flat surface are received. The equation has integral of collisions BGK (Bhatnagar, Gross and Krook) and constant frequency of collisions of molecules. Distribution of concentration, mass speed and temperature is received.

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