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arXiv · 2106.11163

Energy-dissipation for time-fractional phase-field equations

Dong Li·Chaoyu Quan·Jiao Xu
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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.

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Dong Li, Chaoyu Quan, Jiao Xu. 2021-06-21. Energy-dissipation for time-fractional phase-field equations. https://arxiv.org/abs/2106.11163

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