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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}
}

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19 pages