{"title":"具有任意数量空间和时间尺度的单调抛物问题的同质化","authors":"Tatiana Danielsson, Liselott Flodén, Pernilla Johnsen, Marianne Olsson Lindberg","doi":"10.21136/AM.2023.0269-22","DOIUrl":null,"url":null,"abstract":"<div><p>We prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of the scale parameter <i>ε</i>. The main tools for the homogenization procedure are multiscale convergence and very weak multiscale convergence, both adapted to evolution problems.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 1","pages":"1 - 24"},"PeriodicalIF":0.6000,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Homogenization of monotone parabolic problems with an arbitrary number of spatial and temporal scales\",\"authors\":\"Tatiana Danielsson, Liselott Flodén, Pernilla Johnsen, Marianne Olsson Lindberg\",\"doi\":\"10.21136/AM.2023.0269-22\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of the scale parameter <i>ε</i>. The main tools for the homogenization procedure are multiscale convergence and very weak multiscale convergence, both adapted to evolution problems.</p></div>\",\"PeriodicalId\":55505,\"journal\":{\"name\":\"Applications of Mathematics\",\"volume\":\"69 1\",\"pages\":\"1 - 24\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-12-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applications of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.21136/AM.2023.0269-22\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applications of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.21136/AM.2023.0269-22","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Homogenization of monotone parabolic problems with an arbitrary number of spatial and temporal scales
We prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of the scale parameter ε. The main tools for the homogenization procedure are multiscale convergence and very weak multiscale convergence, both adapted to evolution problems.
期刊介绍:
Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering.
The main topics covered include:
- Mechanics of Solids;
- Fluid Mechanics;
- Electrical Engineering;
- Solutions of Differential and Integral Equations;
- Mathematical Physics;
- Optimization;
- Probability
Mathematical Statistics.
The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.