Banasiak, JacekJoel, L.O.Shindin, S.2018-09-112018-11Banasiak J, Joel LO, Shindin S. Analysis and simulations of the discrete fragmentation equation with decay. Mathematical Methods in the Applied Sciences. 2018;41:6530–6545. https://doi.org/10.1002/mma.4666.0170-4214 (print)1099-1476 (online)10.1002/mma.4666http://hdl.handle.net/2263/66520The 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.en© 2017 John Wiley and Sons, Ltd. This is the pre-peer reviewed version of the following article : Analysis and simulations of the discrete fragmentation equation with decay. Mathematical Methods in the Applied Sciences, vol 41, pp. 530–6545, 2018, doi : 10.1002/mma.4666. The definite version is available at : http://wileyonlinelibrary.com/journal/mma.Asynchronous exponential growthC0 semigroupsDeath processDiscrete fragmentationLong-term behaviourNumerical simulationsSpectral gapAggregatesExponential growthNumerical modelsComputer simulationPostprint Article