https://scholars.lib.ntu.edu.tw/handle/123456789/626701
標題: | Refined Description and Stability for Singular Solutions of the 2D Keller-Segel System | 作者: | Collot, C Ghoul, TE Masmoudi, N Van Tien Nguyen |
關鍵字: | II BLOW-UP; RADIALLY SYMMETRIC-SOLUTIONS; CHEMOTAXIS MODEL; POINT DYNAMICS; CRITICAL MASS; AGGREGATION; 8-PI-PROBLEM; MECHANISMS; LIMIT | 公開日期: | 七月-2022 | 出版社: | WILEY | 卷: | 75 | 期: | 7 | 起(迄)頁: | 1419 | 來源出版物: | COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 摘要: | We construct solutions to the two-dimensional parabolic-elliptic Keller-Segel model for chemotaxis that blow up in finite time T. The solution is decomposed as the sum of a stationary state concentrated at scale λ and of a perturbation. We rely on a detailed spectral analysis for the linearised dynamics in the parabolic neighbourhood of the singularity performed by the authors in [10], providing a refined expansion of the perturbation. Our main result is the construction of a stable dynamics in the full nonradial setting for which the stationary state collapses with the universal law. (Formula presented.). where γ is the Euler constant. This improves on the earlier result by Raphael and Schweyer and gives a new robust approach to so-called type II singularities for critical parabolic problems. A by-product of the spectral analysis we developed is the existence of unstable blowup dynamics with speed. (Formula presented.) © 2021 Wiley Periodicals LLC. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/626701 | ISSN: | 0010-3640 | DOI: | 10.1002/cpa.21988 |
顯示於: | 應用數學科學研究所 |
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