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arXiv · 2607.08916

A chemotaxis-consumption model with boundary inflow of a nutrient, steady states

Frederic Heihoff·Piotr Knosalla
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Abstract

In this manuscript we consider the steady state problem for a chemotaxis-consumption model with positive inflow of a nutrient across the boundary. We show that in any bounded smooth domain there exists a unique nonconstant steady state provided that the mass of bacteria is sufficiently large. We further prove that, if the domain is a ball, this condition can be dropped and solutions exist for any positive bacterial mass.

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Frederic Heihoff, Piotr Knosalla. 2026-07-09. A chemotaxis-consumption model with boundary inflow of a nutrient, steady states. https://arxiv.org/abs/2607.08916

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