A toxin-mediated size-structured population model: Finite difference approximation and well-posedness
The question of the effects of environmental toxins on ecological communities is of great interest from both environmental and conservational points of view. Mathematical models have been applied increasingly to predict the effects of toxins on a variety of ecological processes. Motivated by...
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| Language: | English |
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AIMS Press
2016-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016015 |
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| author | Qihua Huang Hao Wang |
| author_facet | Qihua Huang Hao Wang |
| author_sort | Qihua Huang |
| collection | DOAJ |
| description | The question of the effects of environmental toxins on ecological communities is of great interest from both environmental and conservational points of view. Mathematical models have been applied increasingly to predict the effects of toxins on a variety of ecological processes. Motivated by the fact that individuals with different sizes may have different sensitivities to toxins, we develop a toxin-mediated size-structured model which is given by a system of first order fully nonlinear partial differential equations (PDEs). It is very possible that this work represents the first derivation of a PDE model in the area of ecotoxicology. To solve the model, an explicit finite difference approximation to this PDE system is developed. Existence-uniqueness of the weak solution to the model is established and convergence of the finite difference approximation to this unique solution is proved. Numerical examples are provided by numerically solving the PDE model using the finite difference scheme. |
| format | Article |
| id | doaj-art-0f8fc23550f24b95b04a97c9a695e3ab |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-0f8fc23550f24b95b04a97c9a695e3ab2025-01-24T02:36:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-04-0113469772210.3934/mbe.2016015A toxin-mediated size-structured population model: Finite difference approximation and well-posednessQihua Huang0Hao Wang1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1The question of the effects of environmental toxins on ecological communities is of great interest from both environmental and conservational points of view. Mathematical models have been applied increasingly to predict the effects of toxins on a variety of ecological processes. Motivated by the fact that individuals with different sizes may have different sensitivities to toxins, we develop a toxin-mediated size-structured model which is given by a system of first order fully nonlinear partial differential equations (PDEs). It is very possible that this work represents the first derivation of a PDE model in the area of ecotoxicology. To solve the model, an explicit finite difference approximation to this PDE system is developed. Existence-uniqueness of the weak solution to the model is established and convergence of the finite difference approximation to this unique solution is proved. Numerical examples are provided by numerically solving the PDE model using the finite difference scheme.https://www.aimspress.com/article/doi/10.3934/mbe.2016015toxinfinite difference approximationsize-structured modelexistence-uniqueness. |
| spellingShingle | Qihua Huang Hao Wang A toxin-mediated size-structured population model: Finite difference approximation and well-posedness Mathematical Biosciences and Engineering toxin finite difference approximation size-structured model existence-uniqueness. |
| title | A toxin-mediated size-structured population model: Finite difference approximation and well-posedness |
| title_full | A toxin-mediated size-structured population model: Finite difference approximation and well-posedness |
| title_fullStr | A toxin-mediated size-structured population model: Finite difference approximation and well-posedness |
| title_full_unstemmed | A toxin-mediated size-structured population model: Finite difference approximation and well-posedness |
| title_short | A toxin-mediated size-structured population model: Finite difference approximation and well-posedness |
| title_sort | toxin mediated size structured population model finite difference approximation and well posedness |
| topic | toxin finite difference approximation size-structured model existence-uniqueness. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016015 |
| work_keys_str_mv | AT qihuahuang atoxinmediatedsizestructuredpopulationmodelfinitedifferenceapproximationandwellposedness AT haowang atoxinmediatedsizestructuredpopulationmodelfinitedifferenceapproximationandwellposedness AT qihuahuang toxinmediatedsizestructuredpopulationmodelfinitedifferenceapproximationandwellposedness AT haowang toxinmediatedsizestructuredpopulationmodelfinitedifferenceapproximationandwellposedness |