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arXiv · 2406.18750

Stationary states of a chemotaxis consumption system with singular sensitivity and inhomogeneous boundary conditions

Jaewook Ahn·Johannes Lankeit
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Abstract

For given total mass $m>0$ we show unique solvability of the stationary chemotaxis-consumption model \[ \begin{cases} 0= \Delta u - \chi \nabla \cdot (\frac{u}{v} \nabla v) \\ 0= \Delta v - uv \\ \int_\Omega u = m \end{cases} \] under no-flux-Dirichlet boundary conditions in bounded smooth domains $\Omega\subset \mathbb{R}^2$ and $\Omega=B_R(0)\subset \mathbb{R}^d$, $d\ge 3$.

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Jaewook Ahn, Johannes Lankeit. 2024-06-26. Stationary states of a chemotaxis consumption system with singular sensitivity and inhomogeneous boundary conditions. https://arxiv.org/abs/2406.18750

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