Autor(es): Kaushik, Sonali ; Kumar, Rajesh ; Costa, Fernando Pestana da
Data: 2023
Identificador Persistente: http://hdl.handle.net/10400.2/16780
Origem: Repositório Aberto da Universidade Aberta
Assunto(s): Discrete population balance model; Safronov–Dubovski coagulation equation; Oort–Hulst–Safronov equation; Existence of solutions; Conservation of mass; differentiability
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.
