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arXiv · 2206.01965

Theoretical analysis of a discrete population balance model for sum kernel

Sonali Kaushik·Rajesh Kumar·Fernando P. da Costa
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Abstract

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 $V_{i,j} \leqs i^α+j^α$ where $0 \leqs α\leqs 1$. The article finally deals with the uniqueness result that requires the boundedness of the second moment.

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Sonali Kaushik, Rajesh Kumar, Fernando P. da Costa. 2022-06-04. Theoretical analysis of a discrete population balance model for sum kernel. https://arxiv.org/abs/2206.01965

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