Well-posedness and asymptotic limits for a degenerate Keller-Segel system with volume filling
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913149835280384 |
|---|---|
| author | Geltner, Noah Jüngel, Ansgar Zhang, Mingyue |
| author_facet | Geltner, Noah Jüngel, Ansgar Zhang, Mingyue |
| contents | A class of parabolic-parabolic Keller-Segel systems with degenerate diffusion and volume filling is studied in a bounded domain subject to no-flux boundary conditions. The equations are derived from a multiphase fluid model. The interplay between nonlinear diffusion and density saturation leads to a rich variety of behaviors across different parameter regimes. We establish the existence of global weak solutions, a weak-strong uniqueness result, the exponential convergence to the homogeneous steady state, pattern formation in one spatial dimension, as well as the parabolic-elliptic and vanishing diffusion limits. The analysis relies on a priori estimates derived from suitable entropy functionals. Pattern formation is demonstrated by reducing the system to a first-order equation and conducting a detailed analysis of the resulting nonlinearity. Numerical simulations from a one-dimensional finite-volume scheme illustrate the asymptotic regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21296 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Well-posedness and asymptotic limits for a degenerate Keller-Segel system with volume filling Geltner, Noah Jüngel, Ansgar Zhang, Mingyue Analysis of PDEs 35K51, 35K65, 35B36, 35Q92, 92C17 A class of parabolic-parabolic Keller-Segel systems with degenerate diffusion and volume filling is studied in a bounded domain subject to no-flux boundary conditions. The equations are derived from a multiphase fluid model. The interplay between nonlinear diffusion and density saturation leads to a rich variety of behaviors across different parameter regimes. We establish the existence of global weak solutions, a weak-strong uniqueness result, the exponential convergence to the homogeneous steady state, pattern formation in one spatial dimension, as well as the parabolic-elliptic and vanishing diffusion limits. The analysis relies on a priori estimates derived from suitable entropy functionals. Pattern formation is demonstrated by reducing the system to a first-order equation and conducting a detailed analysis of the resulting nonlinearity. Numerical simulations from a one-dimensional finite-volume scheme illustrate the asymptotic regimes. |
| title | Well-posedness and asymptotic limits for a degenerate Keller-Segel system with volume filling |
| topic | Analysis of PDEs 35K51, 35K65, 35B36, 35Q92, 92C17 |
| url | https://arxiv.org/abs/2605.21296 |