Theoretical analysis of a discrete population balance model with sum kernel

Kaushik, Sonali; Kumar, Rajesh; Costa, Fernando Pestana da

http://hdl.handle.net/10400.2/16780

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Authors

Kaushik, Sonali

Kumar, Rajesh

Costa, Fernando Pestana da

Abstract(s)

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 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.

Keywords

Discrete population balance model Safronov–Dubovski coagulation equation Oort–Hulst–Safronov equation Existence of solutions Conservation of mass differentiability

URI

http://hdl.handle.net/10400.2/16780

Citation

Sonali 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. 343–367