Year: 2026
Type: preprint
Abstract: We study the mass-conserved reaction-diffusion system known as the wave-pinning model, which serves as a minimal framework for describing cell polarity. In this model, the interplay between reaction kinetics and slow diffusion forms a sharp interface that partitions the domain into high- and low-concentration regions. We perform a detailed asymptotic analysis and derive higher-order approximation equations governing the motion of this interface. Our results show that on a fast timescale, the interface evolves via propagating front dynamics, whereas on a slow timescale, it evolves as an area-preserving mean curvature flow. Furthermore, using the derived free boundary problem, we demonstrate that on a significantly slower timescale, an interface whose endpoints lie on the domain boundary drifts along the boundary toward regions of higher curvature. In summary, our analysis reveals that the interface dynamics in the wave-pinning model exhibit a hierarchy of three distinct timescales: wave propagation on a fast timescale, curvature-driven area-preserving evolution on a slow timescale, and motion along the boundary on a significantly slower timescale.
Source: arXiv (Cornell University)
Institutions: University of Miyazaki, Kanazawa University
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Establishment of a combustion model considering the shape of solid fuels and exploration of its applicability towards disaster prevention, Mathematical and numerical analysis of Sobolev gradient flows appearing in interface and materials science, Development of a foundation for discrete complex analysis, 自己駆動体運動を記述する反応拡散系モデルとその数理解析, Singularity analysis of complex functions for describing complex phenomena
OpenAlex ID: W7120164920
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