Cahn-Hilliard方程退化扩散率下的尖锐界面极限
Sharp Interface Limits of the Cahn-Hilliard Equation with Degenerate Mobility
AI总结：
本文通过匹配渐近分析推导了二维退化Cahn-Hilliard方程的尖锐界面极限，揭示了界面运动由表面扩散通量和非线性孔隙介质型体扩散共同驱动，高退化扩散率下体扩散占主导。
摘要：
本文通过匹配渐近分析推导了二维退化Cahn-Hilliard方程的尖锐界面极限，该方程具有多项式双井自由能和二次扩散率。与文献中的某些结果不同，我们的分析表明界面运动由表面扩散通量（与界面曲率的表面拉普拉斯成正比）和非线性孔隙介质型体扩散的额外贡献共同驱动。对于更高退化扩散率，体扩散占主导。尖锐界面模型通过比较扰动松弛率与相场模型的结果进行验证。
英文摘要：
In this work, the sharp interface limit of the degenerate Cahn-Hilliard equation (in two space dimensions) with a polynomial double well free energy and a quadratic mobility is derived via a matched asymptotic analysis involving exponentially large and small terms and multiple inner layers. In contrast to some results found in the literature, our analysis reveals that the interface motion is driven by a combination of surface diffusion flux proportional to the surface Laplacian of the interface curvature and an additional contribution from nonlinear, porous-medium type bulk diffusion, For higher degenerate mobilities, bulk diffusion is subdominant. The sharp interface models are corroborated by comparing relaxation rates of perturbations to a radially symmetric stationary state with those obtained by the phase field model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
