Analysis and simulations of the discrete fragmentation equation with decay

dc.contributor.authorBanasiak, Jacek
dc.contributor.authorJoel, L.O.
dc.contributor.authorShindin, S.
dc.contributor.emailjacek.banasiak@up.ac.zaen_ZA
dc.date.accessioned2018-09-11T09:38:15Z
dc.date.issued2018-11
dc.descriptionThe paper was presented at the BIOMATH 2017 Conference, Skukuza, 25–30.06.2017.en_ZA
dc.description.abstractFragmentation‐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_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.embargo2019-11-15
dc.description.librarianhj2018en_ZA
dc.description.sponsorshipThe 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).en_ZA
dc.description.urihttp://wileyonlinelibrary.com/journal/mmaen_ZA
dc.identifier.citationBanasiak 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.en_ZA
dc.identifier.issn0170-4214 (print)
dc.identifier.issn1099-1476 (online)
dc.identifier.other10.1002/mma.4666
dc.identifier.urihttp://hdl.handle.net/2263/66520
dc.language.isoenen_ZA
dc.publisherWileyen_ZA
dc.rights© 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.en_ZA
dc.subjectAsynchronous exponential growthen_ZA
dc.subjectC0 semigroupsen_ZA
dc.subjectDeath processen_ZA
dc.subjectDiscrete fragmentationen_ZA
dc.subjectLong-term behaviouren_ZA
dc.subjectNumerical simulationsen_ZA
dc.subjectSpectral gapen_ZA
dc.subjectAggregatesen_ZA
dc.subjectExponential growthen_ZA
dc.subjectNumerical modelsen_ZA
dc.subjectComputer simulationen_ZA
dc.titleAnalysis and simulations of the discrete fragmentation equation with decayen_ZA
dc.typePostprint Articleen_ZA

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