Note on a Allen-Cahn equation with Caputo-Fabrizio derivative

Authors : Nguyen Duc Phuong

Pages : 179-185

Doi:10.53006/rna.962068

View : 10 | Download : 9

Publication Date : 2021-09-30

Article Type : Research

Abstract :In this short note, we investigate the Allen-Cahn equation with the appearance of the Caputo-Fabizzio derivative. We obtain a local solution when the initial value is small enough. This is an equation that has many practical applications. The power term in the nonlinear component of the source function and the Caputo-Fabizzio operator combine to make finding the solution space more difficult than the classical problem. We discovered a new technique, connecting Hilbert scale and $L^p$ spaces, to overcome these difficulties. Evaluation of the smoothness of the solution was also performed. The research ideas in this paper can be used for many other models.
Keywords : Allen-Cahn equation, Fractional diffusion equation, Caputo-Fabizzio, regularity