Improved convergence rates for the Hele-Shaw limit in the presence of confining potentials
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915580204810240 |
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| author | David, Noemi Mészáros, Alpár R. Santambrogio, Filippo |
| author_facet | David, Noemi Mészáros, Alpár R. Santambrogio, Filippo |
| contents | Nowadays a vast literature is available on the Hele-Shaw or incompressible limit for nonlinear degenerate diffusion equations. This problem has attracted a lot of attention due to its applications to tissue growth and crowd motion modelling as it constitutes a way to link soft congestion (or compressible) models to hard congestion (or incompressible) descriptions. In this paper, we address the question of estimating the rate of this asymptotics in the presence of external drifts. In particular, we provide improved results in the 2-Wasserstein distance which are global in time thanks to the contractivity property that holds for strictly convex potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved convergence rates for the Hele-Shaw limit in the presence of confining potentials David, Noemi Mészáros, Alpár R. Santambrogio, Filippo Analysis of PDEs Nowadays a vast literature is available on the Hele-Shaw or incompressible limit for nonlinear degenerate diffusion equations. This problem has attracted a lot of attention due to its applications to tissue growth and crowd motion modelling as it constitutes a way to link soft congestion (or compressible) models to hard congestion (or incompressible) descriptions. In this paper, we address the question of estimating the rate of this asymptotics in the presence of external drifts. In particular, we provide improved results in the 2-Wasserstein distance which are global in time thanks to the contractivity property that holds for strictly convex potentials. |
| title | Improved convergence rates for the Hele-Shaw limit in the presence of confining potentials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.07227 |