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

Qihua  Huang; Hao Wang

doi:10.3934/mbe.2016015

Article Contents

2016, Volume 13, Issue 4: 697-722. Doi: 10.3934/mbe.2016015

This issue Previous Article Optimal harvesting policy for the Beverton--Holt model Next Article Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate

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

Qihua Huang^1, and
Hao Wang^2,

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

Received: August 31, 2015

Revised: December 31, 2015

Published: April 2016

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Abstract

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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Mathematics Subject Classification: 35L04, 92F99, 65Z99.

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