Time-Fractional Allen–Cahn Equations: Analysis and Numerical Methods

In this work, we consider a time-fractional Allen–Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order α ∈ ( 0 , 1 ) . First, the well-posedness and (limited) smoothing property are studied, by using the maximal L p regularity of...

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Bibliographic Details
Published in:	Journal of scientific computing Vol. 85; no. 2; p. 42
Main Authors:	Du, Qiang, Yang, Jiang, Zhou, Zhi
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.11.2020 Springer Nature B.V
Subjects:	Algorithms Computational Mathematics and Numerical Analysis Energy dissipation Estimates Free energy Gradient flow Inequality Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Maximum principle Molecular beam epitaxy Numerical analysis Numerical methods Quadratures Regularity Splitting Theoretical 65R20 Energy dissipation 65M70 Error estimate Time-fractional Allen–Cahn Regularity Time stepping scheme
ISSN:	0885-7474, 1573-7691
Online Access:	Get full text
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