{"title":"Burgers方程的周期波冲击解","authors":"Saida Bendaas","doi":"10.1080/25742558.2018.1463597","DOIUrl":null,"url":null,"abstract":"In this paper, we present an new approach for the study of Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parameter and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock-type solution for the cauchy problem of the inviscid burgers equation. The results are formulated in classical mathematics and proved with infinitesimal techniques of nonstandard analysis.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.1000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1463597","citationCount":"11","resultStr":"{\"title\":\"Periodic wave shock solutions of Burgers equations\",\"authors\":\"Saida Bendaas\",\"doi\":\"10.1080/25742558.2018.1463597\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present an new approach for the study of Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parameter and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock-type solution for the cauchy problem of the inviscid burgers equation. The results are formulated in classical mathematics and proved with infinitesimal techniques of nonstandard analysis.\",\"PeriodicalId\":92618,\"journal\":{\"name\":\"Cogent mathematics & statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/25742558.2018.1463597\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cogent mathematics & statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/25742558.2018.1463597\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cogent mathematics & statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/25742558.2018.1463597","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Periodic wave shock solutions of Burgers equations
In this paper, we present an new approach for the study of Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parameter and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock-type solution for the cauchy problem of the inviscid burgers equation. The results are formulated in classical mathematics and proved with infinitesimal techniques of nonstandard analysis.
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