{"title":"周期均匀化导论","authors":"F. Alouges","doi":"10.4036/IIS.2016.A.01","DOIUrl":null,"url":null,"abstract":"These notes contain an introduction of the theory of multiscale analysis and periodic homogenization of PDEs. Basic tools, such as multiscale expansion, 2-scale convergence, and Gamma-convergence are introduced and carefully explained. Application to diffusion equation or porous media are also considered, as well as numerical methods. Exercises are also provided to help the reader to become familiar with the theory.","PeriodicalId":91087,"journal":{"name":"Interdisciplinary information sciences","volume":"22 1","pages":"147-186"},"PeriodicalIF":0.0000,"publicationDate":"2016-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4036/IIS.2016.A.01","citationCount":"4","resultStr":"{\"title\":\"Introduction to Periodic Homogenization\",\"authors\":\"F. Alouges\",\"doi\":\"10.4036/IIS.2016.A.01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"These notes contain an introduction of the theory of multiscale analysis and periodic homogenization of PDEs. Basic tools, such as multiscale expansion, 2-scale convergence, and Gamma-convergence are introduced and carefully explained. Application to diffusion equation or porous media are also considered, as well as numerical methods. Exercises are also provided to help the reader to become familiar with the theory.\",\"PeriodicalId\":91087,\"journal\":{\"name\":\"Interdisciplinary information sciences\",\"volume\":\"22 1\",\"pages\":\"147-186\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-12-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.4036/IIS.2016.A.01\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Interdisciplinary information sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4036/IIS.2016.A.01\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Interdisciplinary information sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4036/IIS.2016.A.01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
These notes contain an introduction of the theory of multiscale analysis and periodic homogenization of PDEs. Basic tools, such as multiscale expansion, 2-scale convergence, and Gamma-convergence are introduced and carefully explained. Application to diffusion equation or porous media are also considered, as well as numerical methods. Exercises are also provided to help the reader to become familiar with the theory.
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