{"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.
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.