A nonlocal regularization of a generalized Busenberg-Travis cross-diffusion system
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914853374918656 |
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| author | Jüngel, Ansgar Vetter, Martin Zurek, Antoine |
| author_facet | Jüngel, Ansgar Vetter, Martin Zurek, Antoine |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01123 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A nonlocal regularization of a generalized Busenberg-Travis cross-diffusion system Jüngel, Ansgar Vetter, Martin Zurek, Antoine Analysis of PDEs 35K20, 35K59, 35Q92, 92D25 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. |
| title | A nonlocal regularization of a generalized Busenberg-Travis cross-diffusion system |
| topic | Analysis of PDEs 35K20, 35K59, 35Q92, 92D25 |
| url | https://arxiv.org/abs/2407.01123 |