Pré-Publication, Document De Travail Année : 2024

A nonlocal regularization of a generalized Busenberg-Travis cross-diffusion system

Résumé

A cross-diffusion system with Lotka--Volterra reaction terms in a bounded domain with no-flux boundary conditions is analyzed. The system is a nonlocal regularization of a generalized Busenberg--Travis model, which describes segregating population species with local averaging. The partial velocities are the solutions of an elliptic regularization of Darcy's law, which can be interpreted as a Brinkman's law. The following results are proved: the existence of global weak solutions; localization limit; boundedness and uniqueness of weak solutions (in one space dimension); exponential decay of the solutions. Moreover, the weak--strong uniqueness property for the limiting system is shown.

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Dates et versions

hal-04630443 , version 1 (01-07-2024)

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Identifiants

  • HAL Id : hal-04630443 , version 1

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Ansgar Jüngel, Martin Vetter, Antoine Zurek. A nonlocal regularization of a generalized Busenberg-Travis cross-diffusion system. 2024. ⟨hal-04630443⟩
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