{"title":"用非齐次monge-ampÈre方程的接触群构造非等熵一维气体运动","authors":"S. Khabirov","doi":"10.1070/SM1992V071N02ABEH001405","DOIUrl":null,"url":null,"abstract":"The equations of one-dimensional gas dynamics in Lagrange coordinates are connected with the inhomogeneous Monge-Ampere equation by means of a differential substitution. A classification of Monge-Ampere equations based on point and contact transformations is carried out. In the case of an infinite group various linearizations of the equations of gas dynamics are presented. New conservation laws are constructed on the basis of Noether's theorem. Examples of invariant solutions with variable entropy are considered, and some boundary value problems with curved shock waves are also solved.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"126 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"NONISENTROPIC ONE-DIMENSIONAL GAS MOTIONS CONSTRUCTED BY MEANS OF THE CONTACT GROUP OF THE NONHOMOGENEOUS MONGE-AMPÈRE EQUATION\",\"authors\":\"S. Khabirov\",\"doi\":\"10.1070/SM1992V071N02ABEH001405\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The equations of one-dimensional gas dynamics in Lagrange coordinates are connected with the inhomogeneous Monge-Ampere equation by means of a differential substitution. A classification of Monge-Ampere equations based on point and contact transformations is carried out. In the case of an infinite group various linearizations of the equations of gas dynamics are presented. New conservation laws are constructed on the basis of Noether's theorem. Examples of invariant solutions with variable entropy are considered, and some boundary value problems with curved shock waves are also solved.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"126 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992V071N02ABEH001405\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V071N02ABEH001405","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
NONISENTROPIC ONE-DIMENSIONAL GAS MOTIONS CONSTRUCTED BY MEANS OF THE CONTACT GROUP OF THE NONHOMOGENEOUS MONGE-AMPÈRE EQUATION
The equations of one-dimensional gas dynamics in Lagrange coordinates are connected with the inhomogeneous Monge-Ampere equation by means of a differential substitution. A classification of Monge-Ampere equations based on point and contact transformations is carried out. In the case of an infinite group various linearizations of the equations of gas dynamics are presented. New conservation laws are constructed on the basis of Noether's theorem. Examples of invariant solutions with variable entropy are considered, and some boundary value problems with curved shock waves are also solved.
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