Theoretical analysis of a discrete population balance model with sum kernel

The Oort-Hulst-Safronov equation is a relevant population balance model. Its discrete form, developed by Pavel Dubovski, is the main focus of our analysis. The existence and density conservation are established for non-negative symmetric coagulation rates satisfying [V.sub.i,j] [less than or equal to] i + j, [for all]i, j [member of] N. Differentiability of the solutions is investigated for kernels with [V.sub.i,j] [less than or equal to] [i.sup.[alpha]] + [j.sup.[alpha]] where 0 [less than or equal to] a [less than or equal to] 1 with initial conditions with bounded (1 + [alpha])-th moments. The article ends with a uniqueness result under an additional assumption on the coagulation kernel and the boundedness of the second moment. Keywords. Discrete population balance model, Safronov-Dubovski coagulation equation, Oort-Hulst-Safronov equation, existence of solutions, conservation of mass, differentiability.