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Global existence of a unique solution and a bimodal travelling wave solution for the 1D particle-reaction-diffusion system

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Title: Global existence of a unique solution and a bimodal travelling wave solution for the 1D particle-reaction-diffusion system
Authors: Okamoto, Mamoru Browse this author
Gotoda, Takeshi Browse this author
Nagayama, Masaharu Browse this author →KAKEN DB
Keywords: self-propelled motion
bimodal travelling wave solution
mathematical modelling
global solvability
Issue Date: 21-May-2021
Publisher: IOP Publishing
Journal Title: Journal of Physics Communications
Volume: 5
Issue: 5
Start Page: 055016
Publisher DOI: 10.1088/2399-6528/ac0100
Abstract: In recent years, a mathematical model for collective motions of a self-propelled material have been introduced on the basis of the experiments and numerical analysis for the model have made progress in theoretical understanding of the mechanism of collective motions. On the other hand, there are few mathematically rigorous studies for the mathematical model. In this study, to provide mathematical justification for the mathematical model and its numerical analysis, we show the global existence of a unique solution of the mathematical model for a self-propelled motion on R. Moreover, we give sufficient conditions for the existence of a non-trivial travelling solution on R, which we call a bimodal travelling wave solution.
Rights: http://creativecommons.org/licenses/by/4.0
Type: article
URI: http://hdl.handle.net/2115/82157
Appears in Collections:電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

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