Title  A Decreasing Upper Bound of the Energy for TimeFractional PhaseField Equations 
Author  
Corresponding Author  Wang，Boyi 
Publication Years  20230401

DOI  
Source Title  
ISSN  18152406

EISSN  19917120

Volume  33Issue:4Pages:962991 
Abstract  In this article, we study the energy dissipation property of timefractional AllenCahn equation. On the continuous level, we propose an upper bound of energy that decreases with respect to time and coincides with the original energy at t=0 and as t tends to ∞. This upper bound can also be viewed as a nonlocalintime modified energy which is the summation of the original energy and an accumulation term due to the memory effect of timefractional derivative. In particular, the decrease of the modified energy indicates that the original energy indeed decays w.r.t. time in a small neighborhood at t=0. We illustrate the theory mainly with the timefractional Allen Cahn equation but it could also be applied to other timefractional phasefield models such as the CahnHilliard equation. On the discrete level, the decreasing upper bound of energy is useful for proving energy dissipation of numerical schemes. Firstorder L1 and secondorder L2 schemes for the timefractional AllenCahn equation have similar decreasing modified energies, so that stability can be established. Some numerical results are provided to illustrate the behavior of this modified energy and to verify our theoretical results. 
Keywords  
URL  [Source Record] 
Indexed By  
Language  English

SUSTech Authorship  First
; Corresponding

Funding Project  National Natural Science Foundation of China/Hong Kong RGC Joint Research Scheme[NSFC/RGC 11961160718]
; Guangdong Provincial Key Laboratory of Computational Science And Material Design[2019B030301001]
; National Science Foundation of China (NSFC)[12271241]
; NSFC[2023B1515020030]
; Guangdong Basic and Applied Basic Research Foundation[RCYX20210609104358076]
; Shenzhen Science and Technology Program[UIC 2022B1212010006]
; null[12271240]

WOS Research Area  Physics

WOS Subject  Physics, Mathematical

WOS Accession No  WOS:000993886300002

Publisher  
Scopus EID  2s2.085161279707

Data Source  Scopus

Citation statistics 
Cited Times [WOS]:0

Document Type  Journal Article 
Identifier  http://kc.sustech.edu.cn/handle/2SGJ60CL/560004 
Department  Southern University of Science and Technology 理学院_数学系 
Affiliation  1.International Center for Mathematics,Southern University of Science and Technology,Shenzhen,518055,China 2.Division of Science and Technology,BNUHKBU United International College,Zhuhai,519087,China 3.Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science,BNUHKBU United International College,Zhuhai,519087,China 4.Department of Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China 5.Department of Mathematics,National University of Singapore,Singapore,119076,Singapore 6.Guangdong Provincial Key Laboratory of Computational Science and Material Design,Southern University of Science and Technology,Shenzhen,518055,China 
First Author Affilication  Southern University of Science and Technology 
Corresponding Author Affilication  Department of Mathematics 
First Author's First Affilication  Southern University of Science and Technology; Department of Mathematics 
Recommended Citation GB/T 7714 
Quan，Chaoyu,Tang，Tao,Wang，Boyi,et al. A Decreasing Upper Bound of the Energy for TimeFractional PhaseField Equations[J]. Communications in Computational Physics,2023,33(4):962991.

APA 
Quan，Chaoyu,Tang，Tao,Wang，Boyi,&Yang，Jiang.(2023).A Decreasing Upper Bound of the Energy for TimeFractional PhaseField Equations.Communications in Computational Physics,33(4),962991.

MLA 
Quan，Chaoyu,et al."A Decreasing Upper Bound of the Energy for TimeFractional PhaseField Equations".Communications in Computational Physics 33.4(2023):962991.

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