Caraffini G. L.
Ukr. Mat. Zh. - 2006. - 58, № 3. - pp. 371–380
The problem of the existence of solutions of the hierarchy for the sequence of correlation functions is investigated in the direct sum of spaces of summable functions. We prove the existence and uniqueness of solutions, which are represented through a semigroup of bounded strongly continuous operators. The infinitesimal generator of the semigroup coincides on a certain everywhere dense set with the operator on the right-hand side of the hierarchy. For initial data from this set, solutions are strong; for general initial data, they are generalized ones.
Analog of the Liouville Equation and BBGKY Hierarchy for a System of Hard Spheres with Inelastic Collisions
Ukr. Mat. Zh. - 2005. - 57, № 6. - pp. 818–839
Dynamics of a system of hard spheres with inelastic collisions is investigated. This system is a model for granular flow. The map induced by a shift along the trajectory does not preserve the volume of the phase space, and the corresponding Jacobian is different from one. A special distribution function is defined as the product of the usual distribution function and the squared Jacobian. For this distribution function, the Liouville equation with boundary condition is derived. A sequence of correlation functions is defined for canonical and grand canonical ensemble. The generalized BBGKY hierarchy and boundary condition are deduced for correlation functions.