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The moving-boundary (MB) model is derived on the basis of physical and phenomenological considerations. A center manifold theory for the MB model is developed in this chapter. Consequently, under the assumption that the camphor disk is sufficiently slow, a system of ordinary differential equations is derived from the MB model in a mathematically rigorous manner. Ordinary differential equations that describe the interaction of two disks are also derived.

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Mathematical Modeling, Simulation, and Analysis

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  • 发表日期：

    2026年

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  • Tomoyuki Miyaji,
  • Shin-Ichiro Ei,
  • Masayasu Mimura

摘要

The moving-boundary (MB) model is derived on the basis of physical and phenomenological considerations. A center manifold theory for the MB model is developed in this chapter. Consequently, under the assumption that the camphor disk is sufficiently slow, a system of ordinary differential equations is derived from the MB model in a mathematically rigorous manner. Ordinary differential equations that describe the interaction of two disks are also derived.