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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.16894 |
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| _version_ | 1866915563236753408 |
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| author | de Courcel, Antonin Chodron Elbar, Charles |
| author_facet | de Courcel, Antonin Chodron Elbar, Charles |
| contents | We study a scalar conservation law on the torus in which the flux $\mathbf{j}$ is composed of a Coulomb interaction and a nonlinear mobility: $\mathbf{j} = -u^m\nabla\mathsf{g}\ast u$. We prove existence of entropy solutions and a weak-strong uniqueness principle. We also prove several properties shared among entropy solutions, in particular a lower barrier in the fast diffusion regime $m\lt 1$. In the porous media regime $m\ge 1$, we study the decreasing rearrangement of solutions, which allows to prove an instantaneous growth of the support and a waiting time phenomenon. We also show exponential convergence of the solutions towards the spatial average in several topologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16894 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a repulsion model with Coulomb interaction and nonlinear mobility de Courcel, Antonin Chodron Elbar, Charles Analysis of PDEs Mathematical Physics We study a scalar conservation law on the torus in which the flux $\mathbf{j}$ is composed of a Coulomb interaction and a nonlinear mobility: $\mathbf{j} = -u^m\nabla\mathsf{g}\ast u$. We prove existence of entropy solutions and a weak-strong uniqueness principle. We also prove several properties shared among entropy solutions, in particular a lower barrier in the fast diffusion regime $m\lt 1$. In the porous media regime $m\ge 1$, we study the decreasing rearrangement of solutions, which allows to prove an instantaneous growth of the support and a waiting time phenomenon. We also show exponential convergence of the solutions towards the spatial average in several topologies. |
| title | On a repulsion model with Coulomb interaction and nonlinear mobility |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2510.16894 |