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Energy-dissipation for time-fractional phase-field equations (2106.11163v1)
Published 21 Jun 2021 in math.AP, cs.NA, and math.NA
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.