Stability of the critical constant steady state of a Keller--Segel model

Nobuhito Miyake; Hiroshi Wakui; Tetsuya Yamada

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arXiv · 2606.12227

Stability of the critical constant steady state of a Keller--Segel model

Nobuhito Miyake·Hiroshi Wakui·Tetsuya Yamada

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Abstract

In this paper, we prove the asymptotic stability of the critical constant steady state for a simplified parabolic--elliptic Keller--Segel system in $\mathbb{R}^N$ ($N \ge 3$), which admits a one-parameter family of constant steady states. Although the stability threshold for constant steady states is known, the critical case has remained open. We also show that the convergence rate in the critical case differs from the rates obtained for previously studied subcritical constant steady states.

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Nobuhito Miyake, Hiroshi Wakui, Tetsuya Yamada. 2026-06-10. Stability of the critical constant steady state of a Keller--Segel model. https://arxiv.org/abs/2606.12227

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