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_{i,j} \leqslant i+j , \forall i,j \in \mathbb{N} . Differentiability of the solutions is investigated for kernels with V_{i,j} \leqslant i^{\alpha}+j^{\alpha} where 0 \leqslant \alpha \leqslant 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.