Existence and uniqueness for a kinetic model of population dynamics with character dependence and spatial structure |
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| Authors: | Bedr'Eddine Ainseba Ahmed Noussair |
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| Institution: | a UMR CNRS 5466, Mathématiques Appliquées de Bordeaux, Case 26, Université Victor Segalen Bordeaux 2, 146 rue Léo-Saignat, 33076 Bordeaux Cedex, France
b UMR CNRS 5466 Mathématiques Appliquées de Bordeaux, Université Bordeaux 1 351 cours de la Libération, 33405 Talence, France |
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| Abstract: | In this work, we consider a one species population dynamics model with character dependence, spatial structure and a nonlocal renewal process arising as a boundary condition. The individual interaction are based on Boltzmann kinetic-type modeling. Using fixed point arguments and the div-rot lemma, we prove that our model admits a unique global nonnegative solution. |
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| Keywords: | Population dynamics Diffusion Kinetic models Nonlocal boundary conditions Quadratic integro-differential interactions |
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