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Mathematical Biosciences and Engineering

2015, Volume 12, Issue 2: 233-258. doi: 10.3934/mbe.2015.12.233
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Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model

  • 1.
    Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010
  • 2.
    Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205
  • Received: 01 April 2014 Accepted: 29 June 2018 Published: 01 December 2014

  • MSC : Primary: 35A05, 35D05, 35F25, 35L67, 92D25.

  • We study a quasilinear hierarchically size-structured population modelpresented in [4]. In this model the growth, mortality andreproduction rates are assumed to depend on a function of thepopulation density. In [4] we showed that solutions to thismodel can become singular (measure-valued) in finite time even ifall the individual parameters are smooth. Therefore, in this paperwe develop a first order finite difference scheme to compute thesemeasure-valued solutions. Convergence analysis for this method isprovided. We also develop a high resolution second order scheme tocompute the measure-valued solution of the model and perform a comparative study between thetwo schemes.

    Citation: Azmy S. Ackleh, Vinodh K. Chellamuthu, Kazufumi Ito. Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model[J]. Mathematical Biosciences and Engineering, 2015, 12(2): 233-258. doi: 10.3934/mbe.2015.12.233

    Related Papers:

  • We study a quasilinear hierarchically size-structured population modelpresented in [4]. In this model the growth, mortality andreproduction rates are assumed to depend on a function of thepopulation density. In [4] we showed that solutions to thismodel can become singular (measure-valued) in finite time even ifall the individual parameters are smooth. Therefore, in this paperwe develop a first order finite difference scheme to compute thesemeasure-valued solutions. Convergence analysis for this method isprovided. We also develop a high resolution second order scheme tocompute the measure-valued solution of the model and perform a comparative study between thetwo schemes.


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    [1] Theor. Popul. Biol., 71 (2007), 290-300.
    [2] Appl. Math. Optim., 51 (2005), 35-59.
    [3] J. Num. Funct. Anal. Optimization, 18 (1997), 865-884.
    [4] J. Differential Equations, 217 (2005), 431-455.
    [5] Dynamic Systems Appl., 9 (2000), 527-539.
    [6] J. Math. Biol., 35 (1997), 967-987.
    [7] J. Differetial Equations, 252 (2012), 3245-3277.
    [8] Math. Models Methods Appl. Sci., 24 (2014), 2171-2197.
    [9] J. Math. Biol., 32 (1994), 705-729.
    [10] J. Math. Biol., 43 (2001), 157-189.
    [11] Num. Meth. Partial Diff. Eq., 30 (2014), 1797-1820.
    [12] J. Differential Equations, 248 (2010), 2703-2735.
    [13] J. Math. Biol., 34 (1996), 755-772.
    [14] Natural Resource Modeling, 14 (2001), 45-70.
    [15] Mat. Sb., 123 (1970), 228-255; English transl. in Math. USSR Sb., 10 (1970), 217-273.
    [16] SIAM J. Numer. Anal., 45 (2007), 352-370.
    [17] J. Comput. Phys., 77 (1988), 439-471.
    [18] Springer-Verlag, New York, 1994.
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  • © 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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