Numerical solutions of the Allen–Cahn equation with the p-Laplacian
作者：
Highlights：
• The dynamics of the p-Laplacian Allen-Cahn equation is studied numerically.
• Boundedness of the solutions and energy decay properties are analyzed.
• We numerically verify the basic properties of the Allen-Cahn equation are preserved.
• Comparison between classical, fractional, and p-Laplacian operators is presented.
• Eigenvectors and eigenvalues of the discrete p-Laplacian are investigated.
摘要
•The dynamics of the p-Laplacian Allen-Cahn equation is studied numerically.•Boundedness of the solutions and energy decay properties are analyzed.•We numerically verify the basic properties of the Allen-Cahn equation are preserved.•Comparison between classical, fractional, and p-Laplacian operators is presented.•Eigenvectors and eigenvalues of the discrete p-Laplacian are investigated.
论文关键词：p-Laplacian Operator,Finite differences,Allen–Cahn equation,Boundedness of solution,Discrete energy dissipation
论文评审过程：Received 7 March 2022, Revised 4 July 2022, Accepted 19 July 2022, Available online 7 August 2022, Version of Record 7 August 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127435
