Aggregation-Confinement-Diffusion Evolutions with Saturation: Regularity and Long-Time Asymptotics
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912627914964992 |
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| author | Alamri, Yousef |
| author_facet | Alamri, Yousef |
| contents | We establish Hölder regularity for the weak solution to a degenerate diffusion equation in the presence of a local (drift) potential and nonlocal (interaction) term, posed in a bounded domain with no-flux boundary conditions. The degeneracy is due to saturation, i.e., it occurs when the solution reaches its maximal value. As a byproduct of the established regularity and the underlying dissipative structure of the evolution, we prove the uniform convergence of contractive solutions to a stationary state as $t \to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18571 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Aggregation-Confinement-Diffusion Evolutions with Saturation: Regularity and Long-Time Asymptotics Alamri, Yousef Analysis of PDEs 35B65, 35B40, 35K65, 35B45 We establish Hölder regularity for the weak solution to a degenerate diffusion equation in the presence of a local (drift) potential and nonlocal (interaction) term, posed in a bounded domain with no-flux boundary conditions. The degeneracy is due to saturation, i.e., it occurs when the solution reaches its maximal value. As a byproduct of the established regularity and the underlying dissipative structure of the evolution, we prove the uniform convergence of contractive solutions to a stationary state as $t \to \infty$. |
| title | Aggregation-Confinement-Diffusion Evolutions with Saturation: Regularity and Long-Time Asymptotics |
| topic | Analysis of PDEs 35B65, 35B40, 35K65, 35B45 |
| url | https://arxiv.org/abs/2501.18571 |