Analysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamics

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dc.contributor.advisorBanasiak, Jaceken_ZA
dc.contributor.advisorRewitzky, Ingriden_ZA
dc.contributor.authorOmari, Mohameden_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Mathematics Division.en_ZA
dc.date.accessioned2011-11-23T14:41:21Zen_ZA
dc.date.accessioned2011-12-05T12:59:20Z
dc.date.available2011-11-23T14:41:21Zen_ZA
dc.date.available2011-12-05T12:59:20Z
dc.date.issued2011-12en_ZA
dc.descriptionThesis (MSc)--Stellenbosch University, 2011.en_ZA
dc.description.abstractENGLISH ABSTRACT: An integro-differential equation describing the dynamical behaviour of phytoplankton cells is considered in which the effects of cell division and aggregation are incorporated by coupling the coagulation-fragmentation equation with growth, and the McKendrick-von Foerster renewal model of an age-structured population. Under appropriate conditions on the model parameters, the associated initial-boundary value problem is shown to be well posed in a physically relevant Banach space using the theory of strongly continuous semigroups of operators, the theory of perturbation of positive semigroups and the semilinear abstract Cauchy problems theory. In particular, we provide sufficient conditions for honesty of the model. Finally, the results on the effects of the growth-fragmentation-coagulation on the overall evolution of the phytoplankton population are summarised.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: ’n Integro-differensiaalvergelyking wat die dinamiese ontwikkeling van fitoplanktonselle beskryf, word beskou. Die uitwerking van seldeling en -aggregasie is geïnkorporeer deur die vergelyking van koagulasie en fragmentasie met groeiaan die McKendrick-von Foerster hernuwingsmodel van ’n ouderdomsgestruktureerde populasie te koppel. Die teorie van sterk kontinue semigroepe van operatore, steuringsteorie van positiewe semigroepe en die teorie van semilineêre abstrakte Cauchy probleme word aangewend om, onder gepaste voorwaardes met betrekking tot die model se parameters, te bewys dat die geassosieerde beginwaarde-probleem met randvoorwaardes ‘goed gestel’ is in ’n fisies relevante Banach-ruimte. In die besonder word voldoende voorwaardes vir eerlikheid van die model verskaf. Ten slotte word ’n opsomming van die resultate met betrekking tot die gekombineerde uitwerking van groei-fragmentasie- koagulasie op die gesamentlike ontwikkeling van die fitoplanktonpopulasie verskaf.af_ZA
dc.format.extent45 p.
dc.identifier.urihttp://hdl.handle.net/10019.1/17793en_ZA
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch University
dc.subjectMathematical biologyen_ZA
dc.subjectLinear semi-group theoryen_ZA
dc.subjectFragmentation modelen_ZA
dc.subjectPhytoplankton dynamicsen_ZA
dc.subjectDissertations -- Mathematicsen_ZA
dc.subjectTheses -- Mathematicsen_ZA
dc.subjectCoagulationen_ZA
dc.subjectMathematical modelsen_ZA
dc.titleAnalysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamicsen_ZA
dc.typeThesis
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