Energy-dissipation for time-fractional phase-field equations
Analysis of PDEs
2021-06-22 v1 Numerical Analysis
Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2106.11163,
title = {Energy-dissipation for time-fractional phase-field equations},
author = {Dong Li and Chaoyu Quan and Jiao Xu},
journal= {arXiv preprint arXiv:2106.11163},
year = {2021}
}
Comments
19 pages