Homogenization of Non-Autonomous Operators of Convolution Type in Periodic Media

IF 0.4 4区 数学 Q4 STATISTICS & PROBABILITY
A. Piatnitski, E. Zhizhina
{"title":"Homogenization of Non-Autonomous Operators of Convolution Type in Periodic Media","authors":"A. Piatnitski, E. Zhizhina","doi":"10.61102/1024-2953-mprf.2023.29.2.001","DOIUrl":null,"url":null,"abstract":"The paper deals with periodic homogenization problem for a para- bolic equation whose elliptic part is a convolution type operator with rapidly oscillating coefficients. It is assumed that the coefficients are rapidly oscillating periodic functions both in spatial and temporal variables and that the scal- ing is diffusive, that is, the scaling factor of the temporal variable is equal to the square of the scaling factor of the spatial variable. Under the assumption that the convolution kernel has a nite second moment and that the operator is symmetric in spatial variables we show that the equation under study ad- mits homogenization, and we prove that the limit operator is a second order differential parabolic operator with constant coefficients.","PeriodicalId":48890,"journal":{"name":"Markov Processes and Related Fields","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Markov Processes and Related Fields","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.61102/1024-2953-mprf.2023.29.2.001","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1

Abstract

The paper deals with periodic homogenization problem for a para- bolic equation whose elliptic part is a convolution type operator with rapidly oscillating coefficients. It is assumed that the coefficients are rapidly oscillating periodic functions both in spatial and temporal variables and that the scal- ing is diffusive, that is, the scaling factor of the temporal variable is equal to the square of the scaling factor of the spatial variable. Under the assumption that the convolution kernel has a nite second moment and that the operator is symmetric in spatial variables we show that the equation under study ad- mits homogenization, and we prove that the limit operator is a second order differential parabolic operator with constant coefficients.
周期介质中卷积型非自治算子的均匀化
研究一类椭圆部分为快速振荡系数的卷积型算子的准曲型方程的周期均匀化问题。假设系数在空间变量和时间变量中都是快速振荡的周期函数,并且尺度是扩散的,即时间变量的尺度因子等于空间变量的尺度因子的平方。在卷积核有二阶矩和算子在空间变量上对称的假设下,证明了所研究的方程可以齐次化,并证明了极限算子是常系数二阶微分抛物算子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Markov Processes and Related Fields
Markov Processes and Related Fields STATISTICS & PROBABILITY-
CiteScore
0.70
自引率
0.00%
发文量
0
期刊介绍: Markov Processes And Related Fields The Journal focuses on mathematical modelling of today''s enormous wealth of problems from modern technology, like artificial intelligence, large scale networks, data bases, parallel simulation, computer architectures, etc. Research papers, reviews, tutorial papers and additionally short explanations of new applied fields and new mathematical problems in the above fields are welcome.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信