On the existence of a singular limit equation for a model of a self-propelled object motion
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911695208710144 |
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| author | Nagayama, Masaharu Sakakibara, Koya Takasao, Keisuke |
| author_facet | Nagayama, Masaharu Sakakibara, Koya Takasao, Keisuke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the existence of a singular limit equation for a model of a self-propelled object motion Nagayama, Masaharu Sakakibara, Koya Takasao, Keisuke Analysis of PDEs 35K57, 53E10 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. |
| title | On the existence of a singular limit equation for a model of a self-propelled object motion |
| topic | Analysis of PDEs 35K57, 53E10 |
| url | https://arxiv.org/abs/2507.16447 |