A general nonlinear model for the interaction of a size-structured population and its environment: well-posedness and approximation (Q2821876)

This work considers mathematically a system of hyperbolic partial differential equations, which is associated with the dynamics of structured population via assigning its ``spatial variable'' to a continuously distributed characteristic, e.g. age. For the formulated system of equations, an existence and a uniqueness of its weak solution for the discrete finite difference approximation are proven (such a discretization could have sense not only for numerical solution procedures but also for the consideration subpopulations distinguished by coarse steps of the considered parameter characterizing the population's structure). As possible future applications, the blood cells dynamics (erythropoiesis), amphibian and grapevine moth dynamics are proposed but without presentation and discussion of solutions, which correspond to real biological data.