Mathematical problems of statistical mechanics of a system of elastic balls.

*(English. Russian original)*Zbl 0746.35049
Russ. Math. Surv. 45, No. 3, 153-211 (1990); translation from Usp. Mat. Nauk 45, No. 3(273), 135-182 (1990).

A series of problems of mathematical statistical mechanics and methods of their solution for an infinite system of elastic balls is considered. These systems are described by Bogolyubov equations investigated by the authors. They give a few versions of derivations of these equations as a chain of evolution equations in specific functional spaces and solve for them the Cauchy problem. In order to describe states of infinite systems, the thermodynamic limit is carried out in solutions of Bogolyubov equations, that means an extension of the evolution operator from the summable functions space to the space of sequences of functions bounded with respect to configuration variables and exponentially decreasing with respect to momentum variables. The last problem considered is a justification of kinetic equations which is formulated as a suitable limit for solutions of Bogolyubov equations and solved for non- equilibrium as well for the equilibrium states.

Reviewer: N.A.Lar’kin (Novosibirsk)

##### MSC:

35Q72 | Other PDE from mechanics (MSC2000) |

82C21 | Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics |

82B21 | Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics |