PreprintarXiv licencearXiv
Stability of the critical constant steady state of a Keller--Segel model
Abstract
In this paper, we prove the asymptotic stability of the critical constant steady state for a simplified parabolic--elliptic Keller--Segel system in ℝN (N ≥ 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.
Versions
Related
- Stability of steady transonic shocks with constant states in 3D rectangular nozzles under small external forces
- Stability and Instability of the Unique Positive Steady State for a Nonlocal Population Equation
- Ground state uniqueness and quantitative stability for the mass-critical Hartree equation
- A Li-Yau and Aronson-Bénilan approach for the Keller-Segel system with critical exponent
- Absence of critical mass phenomena in one-dimensional critical quasilinear Keller-Segel systems
BibTeX
@misc{miyake2026stability,
title = {{Stability of the critical constant steady state of a Keller--Segel model}},
author = {Nobuhito Miyake and Hiroshi Wakui and Tetsuya Yamada},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.12227},
eprint = {2606.12227},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.12227},
}
RIS
TY - UNPB
TI - Stability of the critical constant steady state of a Keller--Segel model
AU - Nobuhito Miyake
AU - Hiroshi Wakui
AU - Tetsuya Yamada
PY - 2026
DA - 2026/06/10
PB - arXiv
DO - 10.48550/arxiv.2606.12227
UR - https://arxiv.org/abs/2606.12227
AB - In this paper, we prove the asymptotic stability of the critical constant steady state for a simplified parabolic--elliptic Keller--Segel system in ℝ^N (N ≥ 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.
ER -