No pattern formation in a quasilinear chemotaxis model with local sensing
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909174307225600 |
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| author | Laurençot, Philippe Trescases, Ariane |
| author_facet | Laurençot, Philippe Trescases, Ariane |
| contents | Convergence to spatially homogeneous steady states is shown for a chemotaxis model with local sensing and possibly nonlinear diffusion when the intrinsic diffusion rate $ϕ$ dominates the inverse of the chemotactic motility function $γ$, in the sense that $(ϕγ)'\ge 0$. This result encompasses and complies with the analysis and numerical simulations performed in Choi \& Kim (2023). The proof involves two steps: first, a Liapunov functional is constructed when $ϕγ$ is non-decreasing. The convergence proof relies on a detailed study of the dissipation of the Liapunov functional and requires additional technical assumptions on $ϕ$ and $γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12166 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | No pattern formation in a quasilinear chemotaxis model with local sensing Laurençot, Philippe Trescases, Ariane Analysis of PDEs Convergence to spatially homogeneous steady states is shown for a chemotaxis model with local sensing and possibly nonlinear diffusion when the intrinsic diffusion rate $ϕ$ dominates the inverse of the chemotactic motility function $γ$, in the sense that $(ϕγ)'\ge 0$. This result encompasses and complies with the analysis and numerical simulations performed in Choi \& Kim (2023). The proof involves two steps: first, a Liapunov functional is constructed when $ϕγ$ is non-decreasing. The convergence proof relies on a detailed study of the dissipation of the Liapunov functional and requires additional technical assumptions on $ϕ$ and $γ$. |
| title | No pattern formation in a quasilinear chemotaxis model with local sensing |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.12166 |