{"title":"拟线性双曲方程平面上的Goursat问题","authors":"V. Korzyuk, O. Kovnatskaya, V. A. Sevastyuk","doi":"10.29235/1561-8323-2022-66-4-391-396","DOIUrl":null,"url":null,"abstract":"A classical solution of the problem for a quasilinear hyperbolic equation in the case of two independent variables with given conditions for the desired function on the characteristic lines is obtained. The problem is reduced to a system of equations with a completely continuous operator. We constructed the unique solution by the method of successive approximations and showed the necessary and sufficient smoothness and matching conditions on given functions.","PeriodicalId":41825,"journal":{"name":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","volume":null,"pages":null},"PeriodicalIF":0.1000,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Goursat’s problem on the plane for a quasilinear hyperbolic equation\",\"authors\":\"V. Korzyuk, O. Kovnatskaya, V. A. Sevastyuk\",\"doi\":\"10.29235/1561-8323-2022-66-4-391-396\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A classical solution of the problem for a quasilinear hyperbolic equation in the case of two independent variables with given conditions for the desired function on the characteristic lines is obtained. The problem is reduced to a system of equations with a completely continuous operator. We constructed the unique solution by the method of successive approximations and showed the necessary and sufficient smoothness and matching conditions on given functions.\",\"PeriodicalId\":41825,\"journal\":{\"name\":\"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2022-09-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29235/1561-8323-2022-66-4-391-396\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29235/1561-8323-2022-66-4-391-396","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
Goursat’s problem on the plane for a quasilinear hyperbolic equation
A classical solution of the problem for a quasilinear hyperbolic equation in the case of two independent variables with given conditions for the desired function on the characteristic lines is obtained. The problem is reduced to a system of equations with a completely continuous operator. We constructed the unique solution by the method of successive approximations and showed the necessary and sufficient smoothness and matching conditions on given functions.
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