Metastable speeds in the fractional Allen–Cahn equation
作者：
Highlights：
• Fractional Allen-Cahn equations exhibit metastable patterns of phase transitions.
• Examples of metastable patterns are configurations of sharp interfaces with alternating orientation.
• Asymptotic analysis of dynamics after formation of metastable patterns.
• Asymptotic formulas for speed and time-to-collision of approaching interfaces depending on parameters.
• Comparative study of metastable behavior especially for low orders of the fractional Laplacian.
• Numerical study of width and time-to-collapse of approaching interfaces with respect to parameters.
摘要
•Fractional Allen-Cahn equations exhibit metastable patterns of phase transitions.•Examples of metastable patterns are configurations of sharp interfaces with alternating orientation.•Asymptotic analysis of dynamics after formation of metastable patterns.•Asymptotic formulas for speed and time-to-collision of approaching interfaces depending on parameters.•Comparative study of metastable behavior especially for low orders of the fractional Laplacian.•Numerical study of width and time-to-collapse of approaching interfaces with respect to parameters.
论文关键词：Fractional Allen Cahn,Metastability,Numerical study,hp-FEM,fractional diffusion,Nonlocal operator
论文评审过程：Received 1 October 2020, Revised 19 February 2021, Accepted 18 April 2021, Available online 30 May 2021, Version of Record 30 May 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126329
