On an exact solution of master equations for the model of reversible growth

The set of master equations for the monomer quasi-chemical reversible-growth model in a heterogeneous open medium material is studied. The exact solution to the master equations is obtained for the case where the velocity constants for the growth and decay reactions are linear in the particle number. It is shown that the model under consideration is canonically invariant w.r.t. the Polya distribution with a time-dependent mean size of the clusters.