Theoretical analysis of a discrete population balance model for sum kernel

2022/06/04 by Kaushik, Sonali, Kumar, Rajesh, da Costa, Fernando P. · 1 citation
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.01965

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), ∀ i,j ∈ 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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• Gelation and Positivity of Solutions to the Discrete Oort--Hulst--Safronov Coagulation Equation

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