Analysis and simulations of the discrete fragmentation equation with decay

The paper was presented at the BIOMATH 2017 Conference, Skukuza, 25–30.06.2017.Fragmentation‐coagulation processes, in which aggregates can break up or get together, often occur together with decay processes in which the components can be removed from the aggregates by a chemical reaction, evaporation, dissolution, or death. In this paper, we consider the discrete decay‐fragmentation equation and prove the existence and uniqueness of physically meaningful solutions to this equation using the theory of semigroups of operators. In particular, we find conditions under which the solution semigroup is analytic, compact, and has the asynchronous exponential growth property. The theoretical analysis is illustrated by a number of numerical simulations.The research and the conference attendance was supported from the funds of the DST/NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering and NRF PhD bursary (LOJ).http://wileyonlinelibrary.com/journal/mma2019-11-15hj2018Mathematics and Applied Mathematic