Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A general nonlinear model for the interaction of a size-structured population and its environment: Well-posedness and approximation


Authors: Azmy S. Ackleh, Baoling Ma and Robert Miller
Journal: Quart. Appl. Math. 74 (2016), 671-704
MSC (2010): Primary 35Q92, 65M06
Published electronically: June 20, 2016
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Abstract: We present a general model for the interaction of a size-structured population with its environment. The vital rates of the individuals are assumed to depend on a number of variables including the total population and the environment. We develop a finite difference approximation for this general model and prove the convergence of the method to the unique weak solution of the nonlinear system of partial differential equations coupled with ordinary differential equations. Potential applications are presented in various fields ranging from blood cell population dynamics to the study of invasive species.


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Additional Information

Azmy S. Ackleh
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504
Email: ackleh@louisiana.edu

Baoling Ma
Affiliation: Department of Mathematics, Millersville University of Pennsylvania, Millersville, Pennsylvania 17551
Email: baoling.ma@millersville.edu

Robert Miller
Affiliation: Engineering Department, C. H. Fenstermaker and Associates, LLC, Lafayette, Louisiana 70508
Email: robert@fenstermaker.com

DOI: https://doi.org/10.1090/qam/1439
Keywords: Structured population model, environment, finite difference approximations, convergence, well-posedness
Received by editor(s): August 2, 2015
Received by editor(s) in revised form: January 20, 2016
Published electronically: June 20, 2016
Additional Notes: This work is supported in part by the National Science Foundation under grant #DMS-1312963.
Article copyright: © Copyright 2016 Brown University


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