Theoretical analysis of a discrete population balance model for sum kernel

The Oort-Hulst-Safronov equation, shorterned as OHS is a relevant population balance model. Its discrete form, developed by Dubovski is the main focus of our analysis. The existence and density conservation are established for the coagulation rate $V_{i,j} \leqs (i+j),$ $\forall i,j \in \mathbb{N}$. Differentiability of the solutions is investigated for the kernel $V_{i,j} \leqs i^{\alpha}+j^{\alpha}$ where $0 \leqs \alpha \leqs 1$. The article finally deals with the uniqueness result that requires the boundedness of the second moment.