南方科技大学知识苑(SUSTech KC): Analysis and numerical methods for nonlocal-in-time Allen-Cahn equation

题名	Analysis and numerical methods for nonlocal-in-time Allen-Cahn equation
作者	Li, Hongwei 1; Yang, Jiang2,3 ; Zhang, Wei 4,5
通讯作者	Yang, Jiang
发表日期	2024-07-01
DOI	10.1002/num.23124
发表期刊	NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 影响因子和分区
ISSN	0749-159X
EISSN	1098-2426
摘要	In this paper, we investigate the nonlocal-in-time Allen-Cahn equation (NiTACE), which incorporates a nonlocal operator in time with a finite nonlocal memory. Our objective is to examine the well-posedness of the NiTACE by establishing the maximal Lp$$ {L}<^>p $$ regularity for the nonlocal-in-time parabolic equations with fractional power kernels. Furthermore, we derive a uniform energy bound by leveraging the positive definite property of kernel functions. We also develop an energy-stable time stepping scheme specifically designed for the NiTACE. Additionally, we analyze the discrete maximum principle and energy dissipation law, which hold significant importance for phase field models. To ensure convergence, we verify the asymptotic compatibility of the proposed stable scheme. Lastly, we provide several numerical examples to illustrate the accuracy and effectiveness of our method.
关键词	asymptotic compatibility energy dissipation law maximum principle nonlocal-in-time Allen-Cahn equation well-posedness
相关链接	[来源记录]
收录类别	SCI ; EI
语种	英语
学校署名	通讯
资助项目	National Natural Science Foundation of China["12226313","12226319"] ; Shandong Provincial Natural Science Foundation["ZR2021MA049","ZR2019BA002"] ; National Natural Science Foundation of China (NSFC)["12271240","12101059"] ; NSFC/Hong Kong RGC Joint Research Scheme[NSFC/RGC 11961160718] ; Shenzhen Natural Science Fund[RCJC20210609103819018] ; Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science["2022B1212010006","R0400001-22"]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:001279840400001
出版者	WILEY
ESI学科分类	ENGINEERING
来源库	Web of Science
引用统计
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/790119
专题	理学院_数学系南方科技大学
作者单位	1.Shandong Normal Univ, Sch Math & Stat, Jinan, Peoples R China 2.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Dept Math, Shenzhen, Peoples R China 3.Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen NCAMS, Shenzhen, Peoples R China 4.BNU HKBU United Int Coll, Guangdong Prov Key Lab Interdisciplinary Res & App, Zhuhai, Peoples R China 5.BNU HKBU United Int Coll, Dept Math Sci, Zhuhai, Peoples R China
通讯作者单位	数学系; 南方科技大学
推荐引用方式 GB/T 7714	Li, Hongwei,Yang, Jiang,Zhang, Wei. Analysis and numerical methods for nonlocal-in-time Allen-Cahn equation[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2024.
APA	Li, Hongwei,Yang, Jiang,&Zhang, Wei.(2024).Analysis and numerical methods for nonlocal-in-time Allen-Cahn equation.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS.
MLA	Li, Hongwei,et al."Analysis and numerical methods for nonlocal-in-time Allen-Cahn equation".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2024).