The discrete unbounded coagulation-fragmentation equation with growth, decay and sedimentation

dc.contributor.authorBanasiak, Jacek
dc.contributor.authorJoel, Luke O.
dc.contributor.authorShindin, Sergey
dc.contributor.emailjacek.banasiak@up.ac.zaen_ZA
dc.date.accessioned2019-12-05T10:35:55Z
dc.date.issued2019-10
dc.description.abstractIn this paper we consider discrete growth-decay-fragmentation equa-tions that describe the size-distribution of clusters that can undergo splitting, growth and decay. The clusters can be for instance animal groups that can split but can also grow, or decrease in size due to birth or death of individuals in the group, or chemical particles where the growth and decay can be due to surface deposition or erosion. We prove that for a large class of such problems the solution semigroup is analytic and compact and thus has the asynchronous exponential growth property; that is, the long term behaviour of any solution is given by a scalar exponential function multiplied by a vector, called the stable population distribution, that are independent on the initial conditions.en_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.embargo2020-10-01
dc.description.librarianhj2019en_ZA
dc.description.sponsorshipDST/NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering, Grant N 8277, and NRF PhD Grantholder Bursary, Grant N 102275 (LOJ)en_ZA
dc.description.urihttps://www.aimsciences.org/journal/1937-5093en_ZA
dc.identifier.citationJacek Banasiak, Luke O. Joel, Sergey Shindin. The discrete unbounded coagulation-fragmentation equation with growth, decay and sedimentation. Kinetic and Related Models, 2019, 12 (5) : 1069-1092. doi: 10.3934/krm.2019040.en_ZA
dc.identifier.issn1937-5093 (print)
dc.identifier.issn1937-5077 (online)
dc.identifier.other10.3934/krm.2019040
dc.identifier.urihttp://hdl.handle.net/2263/72530
dc.language.isoenen_ZA
dc.publisherAmerican Institute of Mathematical Sciencesen_ZA
dc.rights© 2019 American Institute of Mathematical Sciencesen_ZA
dc.subjectDiscrete fragmentationen_ZA
dc.subjectBirth-and-death processen_ZA
dc.subjectC0-semigroupsen_ZA
dc.subjectLong term behaviouren_ZA
dc.subjectAsynchronous exponential growthen_ZA
dc.subjectSpectral gapen_ZA
dc.subjectNumerical simulationsen_ZA
dc.titleThe discrete unbounded coagulation-fragmentation equation with growth, decay and sedimentationen_ZA
dc.typePostprint Articleen_ZA

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