For the Boltzmann and free motion Kinetik Equations klassification of conserving and decreasing functional is proposed. A theorem on the Uniqueness of the Boltzmann H-function is proved: For the Gaz deskribed by the Boltzmann Kinetic Equation Entropy is the Unique functional decreasing in time. A problem of calculation in explicit form of coefficients for Boltzmann equationin in the case of maxwellian molecules is solved, complete number of integrals is written. First descrete velocity models with proper invariants are constructed for Mixtures, in one dimentional case the unique model is found. Asimptotics of spectrum for a certain class of quantum optic Hamiltonians is found, special polinomials are introduced. Representation of general commutative relations are classified. General correspondence principle "Quantum Hamiltonians–Kinetic Equations" is constructed that generalize Landau–Lifshits–Streater correspondence. General theory of conservational laws for quantum hamiltonians and kinetic equations is constructed, that corresponds each other.
Main publications:
On the Connection of the Formulas for Entropy and Stationary Distribution // Journal of Statistical Physics, 1994, vol. 77, no. 5/6 (with Y. Arhipov and A. Klar).
Velocity Inductive Construction for Mixtures // Transport theory and Statistical Physics, 1999, 28(7), 727–742.
Special Polinomials in Problems of Quantum Optics // Modern Physics Letters B, 1995, vol. 9, no. 5, 291–298 (with Yu. Orlov).
A class of Invariants for the Boltzmann equation and the Broadwell model // Eur. Jour. Mech., B/Fluids, 1997, no. 3, 387–399 (with Y. Arhipov, A. Klar, O. Mingalev).
