Unveiling Explicit Patterns: Exact Steady States and Stability in a Confined Chemotaxis Model
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912789116747776 |
|---|---|
| author | Huang, Yue Xue, Ling Zhao, Kun Zheng, Xiaoming |
| author_facet | Huang, Yue Xue, Ling Zhao, Kun Zheng, Xiaoming |
| contents | Inspired by Carrillo-Li-Wang's work [Proc. London Math. Soc., 2021] on stationary solutions to the singular Keller-Segel system, this paper presents a novel family of explicit steady-state solutions for the same model on a bounded interval, expressed in terms of trigonometric and hyperbolic functions. Under Dirichlet boundary conditions and within a biologically stable parameter regime, these solutions, including singular types such as secant and cosecant, are rigorously derived and analyzed. Their stability is established via energy methods, yielding precise thresholds for pattern persistence. These results provide valuable benchmarks for numerical validation and offer insights into boundary-driven pattern formation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21523 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unveiling Explicit Patterns: Exact Steady States and Stability in a Confined Chemotaxis Model Huang, Yue Xue, Ling Zhao, Kun Zheng, Xiaoming Analysis of PDEs 35Q92, 35K51, 35B40, 35B65 Inspired by Carrillo-Li-Wang's work [Proc. London Math. Soc., 2021] on stationary solutions to the singular Keller-Segel system, this paper presents a novel family of explicit steady-state solutions for the same model on a bounded interval, expressed in terms of trigonometric and hyperbolic functions. Under Dirichlet boundary conditions and within a biologically stable parameter regime, these solutions, including singular types such as secant and cosecant, are rigorously derived and analyzed. Their stability is established via energy methods, yielding precise thresholds for pattern persistence. These results provide valuable benchmarks for numerical validation and offer insights into boundary-driven pattern formation. |
| title | Unveiling Explicit Patterns: Exact Steady States and Stability in a Confined Chemotaxis Model |
| topic | Analysis of PDEs 35Q92, 35K51, 35B40, 35B65 |
| url | https://arxiv.org/abs/2512.21523 |