On clogged and fast diffusions in porous media with fractional pressure
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915627576328192 |
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| author | de Courcel, Antonin Chodron |
| author_facet | de Courcel, Antonin Chodron |
| contents | We study the existence and infinite-speed propagation of solutions to models arising in porous media, when the mobility is highly degenerate (inverse power law). The approach is based on maximum principles for the fractional Laplacian, and allows to derive lower bounds on solutions in a straightforward manner. Finally, in the case of clogged porous media, where the mobility vanishes at points of unbounded density, solutions that become instantaneously bounded are constructed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On clogged and fast diffusions in porous media with fractional pressure de Courcel, Antonin Chodron Analysis of PDEs Mathematical Physics We study the existence and infinite-speed propagation of solutions to models arising in porous media, when the mobility is highly degenerate (inverse power law). The approach is based on maximum principles for the fractional Laplacian, and allows to derive lower bounds on solutions in a straightforward manner. Finally, in the case of clogged porous media, where the mobility vanishes at points of unbounded density, solutions that become instantaneously bounded are constructed. |
| title | On clogged and fast diffusions in porous media with fractional pressure |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2501.11645 |