Existence and non-existence of asymmetrically rotating solutions to a mathematical model of self-propelled motion

Mamoru, Okamoto; Takeshi, Gotoda; Masaharu, Nagayama

Japan Journal of Industrial and Applied Mathematics, 2020, 37(3), 883-912

Permalink : https://hdl.handle.net/2115/79204

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https://doi.org/10.1007/s13160-020-00427-x     12

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アクセス権
open access
URI
https://hdl.handle.net/2115/79204
タイトル
Existence and non-existence of asymmetrically rotating solutions to a mathematical model of self-propelled motion
著者
Mamoru, Okamoto ; Takeshi, Gotoda ; Masaharu, Nagayama
著者名
Mamoru, Okamoto
著者名
Takeshi, Gotoda
e-Rad_Researcher
20314289
著者名
Masaharu, Nagayama
言語
英語
キーワード
Camphor model
Asymmetrically rotating solution
Reaction-diffusion system
発行日
2020-09
出版者
Springer
収録物名
Japan Journal of Industrial and Applied Mathematics
巻(号)
37(3)
ページ
883-912
抄録
Mathematical models for self-propelled motions are often utilized for understanding the mechanism of collective motions observed in biological systems. Indeed, several patterns of collective motions of camphor disks have been reported in experimental systems. In this paper, we show the existence of asymmetrically rotating solutions of a two-camphor model and give necessary conditions for their existence and non-existence. The main theorem insists that the function describing the surface tension should have a concave part so that asymmetric motions of two camphor disks appear. Our result provides a clue for the dependence between the surfactant concentration and the surface tension in the mathematical model, which is difficult to be measured in experiments.
資源タイプ
学術雑誌論文
出版タイプ
Version of Record
権利情報
Creative Commons Attribution 4.0 International
PISSN
0916-7005
関連情報 (isIdenticalTo)
出版社版DOI
https://doi.org/10.1007/s13160-020-00427-x