发表机构
Hokkaido University（北海道大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对二维区域中用于细胞极化的体-表面反应扩散系统，采用奇异摄动方法证明了其稳态脉冲解的存在性，其分析可为其他体-表面型系统应用该方法提供指导。
AI 中文摘要
本文证明了二维区域中用于细胞极化的体-表面反应扩散系统的稳态脉冲解的存在性。采用奇异摄动方法，我们构造了中心位于几何相关势的非退化临界点附近的脉冲解，该势以Neumann格林函数表示，正如文献[watanabe2026]中形式上预测的那样。主要分析难点源于格林函数的对数奇异性所诱导的半拉普拉斯算子，导致内部解呈代数衰减而非指数衰减。我们的分析也可为将奇异摄动方法应用于其他体-表面型系统提供有用指导。
英文摘要
In this paper, we prove the existence of stationary pulse solutions for a bulk-surface reaction-diffusion system modeling cell polarization in two-dimensional domains. Using a singular perturbation method, we construct pulse solutions whose centers lie near non-degenerate critical points of a geometry-dependent potential expressed in terms of the Neumann Green's function, as formally predicted in \cite{watanabe2026}. The main analytical difficulty arises from the half-Laplacian induced by the logarithmic singularity of the Green's function, resulting in algebraically rather than exponentially decaying inner solutions. Our analysis may also serve as a useful guide for applying singular perturbation methods to other bulk-surface type systems.
