Theoretical analysis of a discrete population balance model with sum kernel

Abstract

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 $V_{i,j}⩽i+j$, $\forall i,j\in \mathbb{N}$. Differentiability of the solutions is investigated for kernels with $V_{i,j}⩽i^{\alpha }+j^{\alpha }$ where $0⩽\alpha ⩽1$ 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.