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arXiv · 2507.16447

On the existence of a singular limit equation for a model of a self-propelled object motion

Masaharu Nagayama·Koya Sakakibara·Keisuke Takasao
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Abstract

In this paper, a phase-field model is introduced to describe the evolution of a deformable, self-propelled object driven by surface-tension effects. The model couples an Allen-Cahn-type equation, which distinguishes the body from the surrounding fluid, with a reaction-diffusion equation for the surfactant concentration. As the interface-thickness parameter $\varepsilon$ tends to zero, it is shown that the phase-field model converges to a sharp-interface limit coupled with a reaction-diffusion equation. In particular, the normal velocity is given by the mean curvature, surface tension, and volume-preserving effect.

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Masaharu Nagayama, Koya Sakakibara, Keisuke Takasao. 2025-07-22. On the existence of a singular limit equation for a model of a self-propelled object motion. https://arxiv.org/abs/2507.16447

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