Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH 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. / AFRIKAANSE 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/17793 |
| Date | 12 1900 |
| Creators | Omari, Mohamed |
| Contributors | Banasiak, Jacek, Rewitzky, Ingrid, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Mathematics Division. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 45 p. |
| Rights | Stellenbosch University |
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