About the entropic structure of detailed balanced multi-species cross-diffusion equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866916659645644800 |
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| author | Daus, Esther S. Desvillettes, Laurent Dietert, Helge |
| author_facet | Daus, Esther S. Desvillettes, Laurent Dietert, Helge |
| contents | This paper links at the formal level the entropy structure of a multi-species cross-diffusion system of Shigesada-Kawasaki-Teramoto (SKT) type satisfying the detailed balance condition with the entropy structure of a reversible microscopic many-particle Markov process on a discretised space. The link is established by first performing a mean-field limit to a master equation over discretised space. Then the spatial discretisation limit is performed in a completely rigorous way. This by itself provides a novel strategy for proving global existence of weak solutions to a class of cross-diffusion systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_09808 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | About the entropic structure of detailed balanced multi-species cross-diffusion equations Daus, Esther S. Desvillettes, Laurent Dietert, Helge Analysis of PDEs 35K55, 35K57, 35Q92, 60J28, 82C22, 92D25 This paper links at the formal level the entropy structure of a multi-species cross-diffusion system of Shigesada-Kawasaki-Teramoto (SKT) type satisfying the detailed balance condition with the entropy structure of a reversible microscopic many-particle Markov process on a discretised space. The link is established by first performing a mean-field limit to a master equation over discretised space. Then the spatial discretisation limit is performed in a completely rigorous way. This by itself provides a novel strategy for proving global existence of weak solutions to a class of cross-diffusion systems. |
| title | About the entropic structure of detailed balanced multi-species cross-diffusion equations |
| topic | Analysis of PDEs 35K55, 35K57, 35Q92, 60J28, 82C22, 92D25 |
| url | https://arxiv.org/abs/1803.09808 |