Well-posedness of diffusion-aggregation equations with bounded kernels and their mean-field approximations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909226610196480 |
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| author | Chen, Li Nikolaev, Paul Prömel, David J. |
| author_facet | Chen, Li Nikolaev, Paul Prömel, David J. |
| contents | The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence argument to treat the nonlinearity as well as a Moser iteration. Moreover, we prove a quantitative estimate in probability with arbitrary algebraic rate between the approximative interacting particle systems and the approximative McKean-Vlasov SDEs, which implies propagation of chaos for the interacting particle systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13463 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Well-posedness of diffusion-aggregation equations with bounded kernels and their mean-field approximations Chen, Li Nikolaev, Paul Prömel, David J. Analysis of PDEs Probability 35D30, 35Q70, 60K35 The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence argument to treat the nonlinearity as well as a Moser iteration. Moreover, we prove a quantitative estimate in probability with arbitrary algebraic rate between the approximative interacting particle systems and the approximative McKean-Vlasov SDEs, which implies propagation of chaos for the interacting particle systems. |
| title | Well-posedness of diffusion-aggregation equations with bounded kernels and their mean-field approximations |
| topic | Analysis of PDEs Probability 35D30, 35Q70, 60K35 |
| url | https://arxiv.org/abs/2310.13463 |