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August  2019, 24(8): 4547-4628. doi: 10.3934/dcdsb.2019156

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

Applied Mathematics, RheinMain University of Applied Sciences, Wiesbaden Rüsselsheim, Germany

Dedicated to Peter E. Kloeden on occasion of his 70th birthday

Received  September 2018 Revised  April 2019 Published  June 2019

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.

Citation: Thomas Lorenz. Nonlocal hyperbolic population models structured by size and spatial position: Well-posedness. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 4547-4628. doi: 10.3934/dcdsb.2019156
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