Cross-diffusion limits in multispecies kinetic models
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914042748076032 |
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| author | Jüngel, Ansgar Pollino, Annamaria Taguchi, Satoshi |
| author_facet | Jüngel, Ansgar Pollino, Annamaria Taguchi, Satoshi |
| contents | Cross-diffusion systems are formally derived from multispecies kinetic models in the diffusion limit. The first limit in the multispecies BGK model of Gross and Krook leads to a variant of the non-isothermal Maxwell-Stefan equations. The second limit in a BGK model with Brinkman-type force term yields generalized Busenberg-Travis equations, which reduce for constant temperature to the classical Busenberg-Travis system for segregating population species. Entropy equalities are derived for the kinetic and cross-diffusion equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_14046 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cross-diffusion limits in multispecies kinetic models Jüngel, Ansgar Pollino, Annamaria Taguchi, Satoshi Analysis of PDEs 35Q20, 35K40, 35K59, 76P05, 82B40 Cross-diffusion systems are formally derived from multispecies kinetic models in the diffusion limit. The first limit in the multispecies BGK model of Gross and Krook leads to a variant of the non-isothermal Maxwell-Stefan equations. The second limit in a BGK model with Brinkman-type force term yields generalized Busenberg-Travis equations, which reduce for constant temperature to the classical Busenberg-Travis system for segregating population species. Entropy equalities are derived for the kinetic and cross-diffusion equations. |
| title | Cross-diffusion limits in multispecies kinetic models |
| topic | Analysis of PDEs 35Q20, 35K40, 35K59, 76P05, 82B40 |
| url | https://arxiv.org/abs/2509.14046 |