Physiologically structured populations with diffusion and dynamicboundary conditions
We consider a linear size-structured population model with diffusion in thesize-space. Individuals are recruited into the population at arbitrary sizes.We equip the model with generalized Wentzell-Robin (or dynamic) boundaryconditions. This approach allows the modelling of populations in whichindivi...
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AIMS Press
2011-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.503 |
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| author | József Z. Farkas Peter Hinow |
| author_facet | József Z. Farkas Peter Hinow |
| author_sort | József Z. Farkas |
| collection | DOAJ |
| description | We consider a linear size-structured population model with diffusion in thesize-space. Individuals are recruited into the population at arbitrary sizes.We equip the model with generalized Wentzell-Robin (or dynamic) boundaryconditions. This approach allows the modelling of populations in whichindividuals may have distinguished physiological states. We establishexistence and positivity of solutions by showing that solutions are governed bya positive quasicontractive semigroup of linear operators on thebiologically relevant state space. These results are obtained by establishingdissipativity of a suitably perturbed semigroup generator. We also show thatsolutions of the model exhibit balanced exponential growth, that is, our modeladmits a finite-dimensional global attractor. In case of strictly positivefertility we are able to establish that solutions in fact exhibit asynchronousexponential growth. |
| format | Article |
| id | doaj-art-7fb417b82cae4c76bfaf0b8a9b652917 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7fb417b82cae4c76bfaf0b8a9b6529172025-01-24T02:01:39ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-03-018250351310.3934/mbe.2011.8.503Physiologically structured populations with diffusion and dynamicboundary conditionsJózsef Z. Farkas0Peter Hinow1Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LADepartment of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LAWe consider a linear size-structured population model with diffusion in thesize-space. Individuals are recruited into the population at arbitrary sizes.We equip the model with generalized Wentzell-Robin (or dynamic) boundaryconditions. This approach allows the modelling of populations in whichindividuals may have distinguished physiological states. We establishexistence and positivity of solutions by showing that solutions are governed bya positive quasicontractive semigroup of linear operators on thebiologically relevant state space. These results are obtained by establishingdissipativity of a suitably perturbed semigroup generator. We also show thatsolutions of the model exhibit balanced exponential growth, that is, our modeladmits a finite-dimensional global attractor. In case of strictly positivefertility we are able to establish that solutions in fact exhibit asynchronousexponential growth.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.503diffusionstability.semigroups of linear operatorsstructured populationsspectral methodswentzell-robin boundarycondition |
| spellingShingle | József Z. Farkas Peter Hinow Physiologically structured populations with diffusion and dynamicboundary conditions Mathematical Biosciences and Engineering diffusion stability. semigroups of linear operators structured populations spectral methods wentzell-robin boundarycondition |
| title | Physiologically structured populations with diffusion and dynamicboundary conditions |
| title_full | Physiologically structured populations with diffusion and dynamicboundary conditions |
| title_fullStr | Physiologically structured populations with diffusion and dynamicboundary conditions |
| title_full_unstemmed | Physiologically structured populations with diffusion and dynamicboundary conditions |
| title_short | Physiologically structured populations with diffusion and dynamicboundary conditions |
| title_sort | physiologically structured populations with diffusion and dynamicboundary conditions |
| topic | diffusion stability. semigroups of linear operators structured populations spectral methods wentzell-robin boundarycondition |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.503 |
| work_keys_str_mv | AT jozsefzfarkas physiologicallystructuredpopulationswithdiffusionanddynamicboundaryconditions AT peterhinow physiologicallystructuredpopulationswithdiffusionanddynamicboundaryconditions |