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Analysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamics
Thesis (MSc)--Stellenbosch University, 2011.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2011
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| _version_ | 1867614115754672128 |
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| access_status_str | Open Access |
| author | Omari, Mohamed |
| author2 | Banasiak, Jacek |
| author_browse | Banasiak, Jacek Omari, Mohamed |
| author_facet | Banasiak, Jacek Omari, Mohamed |
| author_sort | Omari, Mohamed |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2011. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/17793 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:46:55.034Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2011 |
| publishDateRange | 2011 |
| publishDateSort | 2011 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/17793 Analysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamics Omari, Mohamed Banasiak, Jacek Rewitzky, Ingrid Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Mathematics Division. Mathematical biology Linear semi-group theory Fragmentation model Phytoplankton dynamics Dissertations -- Mathematics Theses -- Mathematics Coagulation Mathematical models 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. 2011-11-23T14:41:21Z 2011-12-05T12:59:20Z 2011-11-23T14:41:21Z 2011-12-05T12:59:20Z 2011-12 Thesis http://hdl.handle.net/10019.1/17793 en_ZA Stellenbosch University 45 p. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Mathematical biology Linear semi-group theory Fragmentation model Phytoplankton dynamics Dissertations -- Mathematics Theses -- Mathematics Coagulation Mathematical models Omari, Mohamed Analysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamics |
| title | Analysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamics |
| title_full | Analysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamics |
| title_fullStr | Analysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamics |
| title_full_unstemmed | Analysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamics |
| title_short | Analysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamics |
| title_sort | analysis of the effects of growth fragmentation coagulation in phytoplankton dynamics |
| topic | Mathematical biology Linear semi-group theory Fragmentation model Phytoplankton dynamics Dissertations -- Mathematics Theses -- Mathematics Coagulation Mathematical models |
| url | http://hdl.handle.net/10019.1/17793 |
| work_keys_str_mv | AT omarimohamed analysisoftheeffectsofgrowthfragmentationcoagulationinphytoplanktondynamics |