Energy-dissipation for time-fractional phase-field equations-Reference-Cited by-同舟云学术

Energy-dissipation for time-fractional phase-field equations

Published:2022 Issue:10 Volume:21 Page:3371
ISSN:1534-0392
Container-title:Communications on Pure and Applied Analysis
language:
Short-container-title:CPAA

Author:

Li Dong¹,Quan Chaoyu²,Xu Jiao²

Affiliation:

1. SUSTech International Center for Mathematics, and Department of Mathematics, Southern University of Science and Technology, Shenzhen, China

2. SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, China

Abstract

<p style='text-indent:20px;'>We consider a class of time-fractional phase field models including the Allen-Cahn and Cahn-Hilliard equations. We establish several weighted positivity results for functionals driven by the Caputo time-fractional derivative. Several novel criterions are examined for showing the positive-definiteness of the associated kernel functions. We deduce strict energy-dissipation for a number of non-local energy functionals, thereby proving fractional energy dissipation laws.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Analysis,General Medicine

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