{"title":"前后抛物线 PDE 的正则化","authors":"Carina Geldhauser","doi":"10.1002/gamm.202470001","DOIUrl":null,"url":null,"abstract":"<p>Forward-backward parabolic equations have been studied since the 1980s, but a mathematically rigorous picture is still far from being established. As quite a number of new papers have appeared recently, we review in this work the current state of the art. We focus our analysis on the status quo regarding the three most common types of regularizations, namely semidiscretization, the viscous approximation, and regularization with higher order spatial derivatives.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"47 4","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470001","citationCount":"0","resultStr":"{\"title\":\"Regularizations of forward-backward parabolic PDEs\",\"authors\":\"Carina Geldhauser\",\"doi\":\"10.1002/gamm.202470001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Forward-backward parabolic equations have been studied since the 1980s, but a mathematically rigorous picture is still far from being established. As quite a number of new papers have appeared recently, we review in this work the current state of the art. We focus our analysis on the status quo regarding the three most common types of regularizations, namely semidiscretization, the viscous approximation, and regularization with higher order spatial derivatives.</p>\",\"PeriodicalId\":53634,\"journal\":{\"name\":\"GAMM Mitteilungen\",\"volume\":\"47 4\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-10-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202470001\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"GAMM Mitteilungen\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/gamm.202470001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"GAMM Mitteilungen","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/gamm.202470001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Regularizations of forward-backward parabolic PDEs
Forward-backward parabolic equations have been studied since the 1980s, but a mathematically rigorous picture is still far from being established. As quite a number of new papers have appeared recently, we review in this work the current state of the art. We focus our analysis on the status quo regarding the three most common types of regularizations, namely semidiscretization, the viscous approximation, and regularization with higher order spatial derivatives.
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