Kaushik, SonaliKumar, RajeshCosta, Fernando Pestana da2024-11-152024-11-152023-05-18Sonali Kaushik, Rajesh Kumar, Fernando P. da Costa, Theoretical analysis of a discrete population balance model with sum kernel. Port. Math. 80 (2023), no. 3/4, pp. 343–367http://hdl.handle.net/10400.2/16780The 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 nonnegative symmetric coagulation rates satisfying V_{i;j} \leq i + j , \forall i, j \in N. Differentiability of the solutions is investigated for kernels with V_{i;j} \leq i^\apha + j^\alpha˛ where 0 \leq \alpha \leq 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.engDiscrete population balance modelSafronov–Dubovski coagulation equationOort–Hulst–Safronov equationExistence of solutionsConservation of massdifferentiabilityjournal article10.4171/pm/2103