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arXiv · 2001.02340

Short-time approximate solutions of an equation modeling a camphor motion

Jishan Fan·Masaharu Nagayama·Gen Nakamura·Masaaki Uesaka
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Abstract

As a profound example of spontaneous motion, we analyze the motion of a camphor particle on a water surface. The motion is modeled as an initial-boundary value problem for a coupled nonlinear system of a diffusion equation and an ordinary differential equation in a two-dimensional domain. Since it seems that the well-posedness of this initial boundary value problem is missing, we provided its proof. Then, by constructing an approximate solution to this initial boundary value problem, we gave a mathematically rigorous interpretation of a camphor motion. That is we showed that the motion of camphor locally in time has a self-avoiding orbit. We also gave the numerical performance of the approximate solution.

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Jishan Fan, Masaharu Nagayama, Gen Nakamura, Masaaki Uesaka. 2020-01-08. Short-time approximate solutions of an equation modeling a camphor motion. https://arxiv.org/abs/2001.02340

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