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Pré-Publication, Document De Travail Année : 2024

NO PATTERN FORMATION IN A QUASILINEAR CHEMOTAXIS MODEL WITH LOCAL SENSING

Résumé

Convergence to spatially homogeneous steady states is shown for a chemotaxis model with local sensing and possibly nonlinear diffusion when the intrinsic diffusion rate $\phi$ dominates the inverse of the chemotactic motility function $\gamma$, in the sense that $(\phi\gamma)'\ge 0$. 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 $\phi\gamma$ is non-decreasing. The convergence proof relies on a detailed study of the dissipation of the Liapunov functional and requires additional technical assumptions on $\phi$ and $\gamma$.
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Dates et versions

hal-04549444 , version 1 (17-04-2024)

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  • HAL Id : hal-04549444 , version 1

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Philippe Laurençot, Ariane Trescases. NO PATTERN FORMATION IN A QUASILINEAR CHEMOTAXIS MODEL WITH LOCAL SENSING. 2024. ⟨hal-04549444⟩
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