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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2105.11389 |
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| _version_ | 1866911172365647872 |
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| author | Fagioli, Simone Tse, Oliver |
| author_facet | Fagioli, Simone Tse, Oliver |
| contents | We prove the well-posedness of entropy solutions for a wide class of nonlocal transport equations with nonlinear mobility in one spatial dimension. The solution is obtained as the limit of approximations constructed via a deterministic system of interacting particles that exhibits a gradient flow structure. At the same time, we expose a rigorous gradient flow structure for this class of equations in terms of an Energy-Dissipation balance, which we obtain via the asymptotic convergence of functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_11389 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility Fagioli, Simone Tse, Oliver Analysis of PDEs We prove the well-posedness of entropy solutions for a wide class of nonlocal transport equations with nonlinear mobility in one spatial dimension. The solution is obtained as the limit of approximations constructed via a deterministic system of interacting particles that exhibits a gradient flow structure. At the same time, we expose a rigorous gradient flow structure for this class of equations in terms of an Energy-Dissipation balance, which we obtain via the asymptotic convergence of functionals. |
| title | On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2105.11389 |