{"title":"非光滑系数线性一阶双曲型微分方程若干解概念的比较","authors":"Simon Haller, G. Hörmann","doi":"10.2298/PIM0898123H","DOIUrl":null,"url":null,"abstract":"We discuss solution concepts for linear hyperbolic equations with coefficients of regularity below Lipschitz continuity. Thereby our focus is on theories which are based either on a generalization of the method of charac- teristics or on refined techniques concerning energy estimates. We provide a series of examples both as simple illustrations of the notions and conditions involved but also to show logical independence among the concepts.","PeriodicalId":416273,"journal":{"name":"Publications De L'institut Mathematique","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"COMPARISON OF SOME SOLUTION CONCEPTS FOR LINEAR FIRST-ORDER HYPERBOLIC DIFFERENTIAL EQUATIONS WITH NON-SMOOTH COEFFICIENTS\",\"authors\":\"Simon Haller, G. Hörmann\",\"doi\":\"10.2298/PIM0898123H\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We discuss solution concepts for linear hyperbolic equations with coefficients of regularity below Lipschitz continuity. Thereby our focus is on theories which are based either on a generalization of the method of charac- teristics or on refined techniques concerning energy estimates. We provide a series of examples both as simple illustrations of the notions and conditions involved but also to show logical independence among the concepts.\",\"PeriodicalId\":416273,\"journal\":{\"name\":\"Publications De L'institut Mathematique\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-12-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Publications De L'institut Mathematique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2298/PIM0898123H\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Publications De L'institut Mathematique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/PIM0898123H","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
COMPARISON OF SOME SOLUTION CONCEPTS FOR LINEAR FIRST-ORDER HYPERBOLIC DIFFERENTIAL EQUATIONS WITH NON-SMOOTH COEFFICIENTS
We discuss solution concepts for linear hyperbolic equations with coefficients of regularity below Lipschitz continuity. Thereby our focus is on theories which are based either on a generalization of the method of charac- teristics or on refined techniques concerning energy estimates. We provide a series of examples both as simple illustrations of the notions and conditions involved but also to show logical independence among the concepts.
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