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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Special Issue: AUS-ICMS 2020   > Article

A Multi-Region Nonlinear Size-Structured Population Model with Coagulation and Vertical Effects

Un modèle de population multirégional et non linéaire structuré par la taille avec coagulation et effets verticaux


Azmy S. Ackleh
University of Louisiana at Lafayette
USA

Robert L. Miller
University of Louisiana at Lafayette
USA



Published on 28 July 2021   DOI : 10.21494/ISTE.OP.2021.0699

Abstract

Résumé

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A general nonlinear model describing the evolution of size-structured populations influenced by coagulation and vertical effects is presented. The nonlinear population dynamics occur in a multi-region setting in which the transfer, coagulation, and vital rates of an individual depend on a vector describing conditions in the environment. The model for these dynamics consists of a system of two-dimensional nonlinear-nonlocal hyperbolic partial differential equations coupled with a system of one-dimensional nonlocal differential equations parametrized by a vertical location coordinate $$${z}$$$ describing the environmental time-dynamics. A finite difference approximation approach is employed to study the wellposedness of the model and convergence of the scheme to the unique weak solution is established. Several examples are presented to illustrate the generality of the model and to motivate applications.

A general nonlinear model describing the evolution of size-structured populations influenced by coagulation and vertical effects is presented. The nonlinear population dynamics occur in a multi-region setting in which the transfer, coagulation, and vital rates of an individual depend on a vector describing conditions in the environment. The model for these dynamics consists of a system of two-dimensional nonlinear-nonlocal hyperbolic partial differential equations coupled with a system of one-dimensional nonlocal differential equations parametrized by a vertical location coordinate $$${z}$$$ describing the environmental time-dynamics. A finite difference approximation approach is employed to study the wellposedness of the model and convergence of the scheme to the unique weak solution is established. Several examples are presented to illustrate the generality of the model and to motivate applications.

multi-region model coagulation vertical effects difference approximations convergence

multi-region model coagulation vertical effects difference approximations convergence