{"title":"弱非线性双曲型系统渐近解的证明","authors":"Aleksandras Krylovas","doi":"10.15388/lmr.2006.30572","DOIUrl":null,"url":null,"abstract":"A hyperbolic system of first order partial differential equations with small parameter and periodical initial conditions is obtained. The uniformly valid in a long time interval asymptotical solution can be constructed using the averaging along characteristics of the system. The asymptotical estimation of the approximation is made in the paper. Some aspects of practical realization of the method are discussed in the work too.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Substantiation of asymptotical solution of weakly nonlinear hyperbolic system\",\"authors\":\"Aleksandras Krylovas\",\"doi\":\"10.15388/lmr.2006.30572\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A hyperbolic system of first order partial differential equations with small parameter and periodical initial conditions is obtained. The uniformly valid in a long time interval asymptotical solution can be constructed using the averaging along characteristics of the system. The asymptotical estimation of the approximation is made in the paper. Some aspects of practical realization of the method are discussed in the work too.\",\"PeriodicalId\":33611,\"journal\":{\"name\":\"Lietuvos Matematikos Rinkinys\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-09-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lietuvos Matematikos Rinkinys\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15388/lmr.2006.30572\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lietuvos Matematikos Rinkinys","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15388/lmr.2006.30572","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Substantiation of asymptotical solution of weakly nonlinear hyperbolic system
A hyperbolic system of first order partial differential equations with small parameter and periodical initial conditions is obtained. The uniformly valid in a long time interval asymptotical solution can be constructed using the averaging along characteristics of the system. The asymptotical estimation of the approximation is made in the paper. Some aspects of practical realization of the method are discussed in the work too.
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