Differential and Integral Equations

A weak solution for a point mass camphor motion

Jishan Fan, Masaharu Nagayama, Gen Nakamura, and Mamoru Okamoto

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

Source
Differential Integral Equations, Volume 33, Number 7/8 (2020), 431-443.

Dates
First available in Project Euclid: 14 July 2020

Permanent link to this document
https://projecteuclid.org/euclid.die/1594692056

Mathematical Reviews number (MathSciNet)
MR4122512

Subjects
Primary: 35K99: None of the above, but in this section 35Q70: PDEs in connection with mechanics of particles and systems

Citation

Fan, Jishan; Nagayama, Masaharu; Nakamura, Gen; Okamoto, Mamoru. A weak solution for a point mass camphor motion. Differential Integral Equations 33 (2020), no. 7/8, 431--443. https://projecteuclid.org/euclid.die/1594692056


Export citation