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2019, Volume 24, Issue 8: 4547-4628. Doi: 10.3934/dcdsb.2019156
This issue Previous Article Mean-square approximations of Lévy noise driven SDEs with super-linearly growing diffusion and jump coefficients Next Article SDE-driven modeling of phenotypically heterogeneous tumors: The influence of cancer cell stemness

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

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

Received:  September 2018
Revised:  April 2019
Early access:  June 2019
Published:  August 2019
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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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