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 Vi,j​⩽i+j, ∀i,j∈N. Differentiability of the solutions is investigated for kernels with Vi,j​⩽iα+jα where 0⩽α⩽1 with initial conditions with bounded (1+α)-th moments. The article ends with a uniqueness result under an additional assumption on the coagulation kernel and the boundedness of the second moment