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, the main focus of our analysis. 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 solutions investigated kernels with i^{\alpha}+j^{\alpha}$ where $0 \alpha 1$ initial conditions bounded $(1+\alpha)$-th moments. article ends uniqueness result under an additional assumption on kernel boundedness second moment.