Energy-dissipation for time-fractional phase-field equations

Dong Li; Chaoyu Quan; Jiao Xu

doi:10.3934/cpaa.2022104

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2022, Volume 21, Issue 10: 3371-3387. Doi: 10.3934/cpaa.2022104

This issue Previous Article Smooth solutions to asymptotic Plateau type problem in hyperbolic space Next Article On the exponential time-decay for the one-dimensional wave equation with variable coefficients

Energy-dissipation for time-fractional phase-field equations

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

^*Corresponding author
^*Corresponding author

Received: March 2022

Early access: June 2022

Published: October 2022

The second author is supported by by NSFC Grant 11901281, the Stable Support Plan Program of Shenzhen Natural Science Fund (Program Contract No. 20200925160747003), and Shenzhen Science and Technology Program (Grant No. RCYX20210609104358076)

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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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Mathematics Subject Classification: Primary: 35R11, 35Q35.

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References

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