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Nonlocal hyperbolic population models structured by size and spatial position: Well-posedness

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  • Detailed models of structured populations are spatial and involve nonlocal effects. These features lead to a broad class of population models structured by a physiological parameter and space. Our focus of interest is on the well-posedness of their initial value problems. In more detail, we specify sufficient conditions on the coefficient functions for existence, positivity, uniqueness of weak solutions and their continuous dependence on the given data. The solutions considered here have their values in $ L^p $ and, all conclusions about convergence and sequential compactness use an adaptation of the KANTOROVICH-RUBINSTEIN metric for this $ L^p $ space.

    Mathematics Subject Classification: Primary: 35L60, 35Q92; Secondary: 35B30, 35L04, 92D25.


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