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arXiv · 2101.01467

Stability of constant steady states of a chemotaxis model

Szymon Cygan·Grzegorz Karch·Krzysztof Krawczyk·Hiroshi Wakui
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Abstract

The Cauchy problem for the parabolic--elliptic Keller--Segel system in the whole $n$-dimensional space is studied. For this model, every constant $A \in \mathbb{R}$ is a stationary solution. The main goal of this work is to show that $A < 1$ is a stable steady state while $A > 1$ is unstable. Uniformly local Lebesgue spaces are used in order to deal with solutions that do not decay at spatial variable on the unbounded domain.

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Szymon Cygan, Grzegorz Karch, Krzysztof Krawczyk, Hiroshi Wakui. 2021-01-05. Stability of constant steady states of a chemotaxis model. https://arxiv.org/abs/2101.01467

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