Finite volume effects in a model grain growth

Usually the distribution function of grains is defined on a semi-axis of all possible sizes of grains. It leads to some inconsistency, because volume of the individual grain can be arbitrary large and can be larger than the total volume of the system as a whole. Therefore in this paper we want to reconsider this problem assuming that the volumes of the individual grains are finite. We regard two classes of the boundary conditions: absorbing and reflecting. For the absorbing conditions, all statistical moments exponentially tend to zero, the stationary state does not exist and the grains-containing system is going to dissolve. In turn, the use of the reflecting boundary conditions realized in a finite size space reveals possibly a phenomenon of practical interest: Existence of a stationary state that depends upon space dimension.