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A toxin-mediated size-structured population model: Finite difference approximation and well-posedness

1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1
2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1

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.
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Keywords toxin; finite difference approximation; Size-structured model; existence-uniqueness.

Citation: Qihua Huang, Hao Wang. A toxin-mediated size-structured population model: Finite difference approximation and well-posedness. Mathematical Biosciences and Engineering, 2016, 13(4): 697-722. doi: 10.3934/mbe.2016015

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This article has been cited by

  • 1. Azmy S. Ackleh, Robert L. Miller, A numerical method for a nonlinear structured population model with an indefinite growth rate coupled with the environment, Numerical Methods for Partial Differential Equations, 2019, 10.1002/num.22418

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Copyright Info: 2016, Qihua Huang, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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