The fractional Allen–Cahn equation with the sextic potential

作者：

Highlights：

• Boundedness of numerical solutions for the fractional Allen – Cahn equation with sextic polynomial is under consideration.

• From the numerical aspect, the inclusion principle is proven to hold only for the Allen – Cahn equation.

• Effects of the fractional order and parameters of the equation is analyzed.

• Eigenvectors of the discrete Laplacian are used for investigating the behaviors of the fractional Allen – Cahn equation.

• The numerical study of the fractional Allen – Cahn equation with the sextic polynomial is verified by various simulations.

摘要

•Boundedness of numerical solutions for the fractional Allen – Cahn equation with sextic polynomial is under consideration.•From the numerical aspect, the inclusion principle is proven to hold only for the Allen – Cahn equation.•Effects of the fractional order and parameters of the equation is analyzed.•Eigenvectors of the discrete Laplacian are used for investigating the behaviors of the fractional Allen – Cahn equation.•The numerical study of the fractional Allen – Cahn equation with the sextic polynomial is verified by various simulations.

论文关键词：Inclusion principle,Solvability,The Allen–Cahn equation,Fractional Laplacian,Sextic free energy polynomial

论文评审过程：Received 1 September 2018, Revised 22 December 2018, Accepted 21 January 2019, Available online 2 February 2019, Version of Record 2 February 2019.

论文官网地址：https://doi.org/10.1016/j.amc.2019.01.037