Analysis of The Discrete Growth-Fragmentation Equation

The discrete case of the growth-fragmentation equation is not as popular in the literature as the continuous form of it, hence the need to explore the discrete version of this model for some interesting analysis. In this paper, We examine the discrete growth-fragmentation equations. The problem is treated as an infinite-dimensional differential equation, posed in a suitable Banach space. Perturbation results, from the theory of strongly continuous semigroups of operators is used for the mathematical analysis of the model. In contrast to the truncation-limit approach, the semigroups of operator approach involves the use of operators to represent the growth-fragmentation model in order to establish the existence and uniqueness of solutions to the model.