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Finite difference approximations for measure-valued solutions of a hierarchically size-structured population model

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  • We study a quasilinear hierarchically size-structured population model presented in [4]. In this model the growth, mortality and reproduction rates are assumed to depend on a function of the population density. In [4] we showed that solutions to this model can become singular (measure-valued) in finite time even if all the individual parameters are smooth. Therefore, in this paper we develop a first order finite difference scheme to compute these measure-valued solutions. Convergence analysis for this method is provided. We also develop a high resolution second order scheme to compute the measure-valued solution of the model and perform a comparative study between the two schemes.
    Mathematics Subject Classification: Primary: 35A05, 35D05, 35F25, 35L67, 92D25.

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