A nonlocal regularization of a generalized Busenberg-Travis cross-diffusion system
Analysis of PDEs
2024-07-02 v1
Abstract
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.
Cite
@article{arxiv.2407.01123,
title = {A nonlocal regularization of a generalized Busenberg-Travis cross-diffusion system},
author = {Ansgar Jüngel and Martin Vetter and Antoine Zurek},
journal= {arXiv preprint arXiv:2407.01123},
year = {2024}
}