July/August 2020 A weak solution for a point mass camphor motion
Jishan Fan, Masaharu Nagayama, Gen Nakamura, Mamoru Okamoto
Differential Integral Equations 33(7/8): 431-443 (July/August 2020). DOI: 10.57262/die/1594692056


The model system of equations which describes the self-propelled motion of point mass objects driven by camphor is a diffusion equation coupled with a system of nonlinear ordinary differential equations. If the objects have masses, then the motion of objects becomes very complicated when some of the objects hit the boundary of a water surface or collide each other. To avoid such complexity and try to get some general perspective for the motion, it is convenient to consider point mass objects, i.e., objects without areas. We give an existence of a weak solution of this model system by giving an a priori estimate for the solution. The key to this estimate is the choice of a special test function. This is a first step toward analyzing collective motion of point mass camphors. As far as we know, this result is the first result on the existence of a weak solution for this system.


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Jishan Fan. Masaharu Nagayama. Gen Nakamura. Mamoru Okamoto. "A weak solution for a point mass camphor motion." Differential Integral Equations 33 (7/8) 431 - 443, July/August 2020. https://doi.org/10.57262/die/1594692056


Published: July/August 2020
First available in Project Euclid: 14 July 2020

zbMATH: 07250701
MathSciNet: MR4122512
Digital Object Identifier: 10.57262/die/1594692056

Primary: 35K99 , 35Q70

Rights: Copyright © 2020 Khayyam Publishing, Inc.


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Vol.33 • No. 7/8 • July/August 2020
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