{"title":"电报方程参数的确定","authors":"A. I. Kozhanov, R. R. Safiullova","doi":"10.13108/2017-9-1-62","DOIUrl":null,"url":null,"abstract":"We study the solvability of the inverse problems on finding a solution u(x, t) and an unknown coefficient c for a telegraph equation utt −Δu+ cu = f(x, t). We prove the theorems on the existence of the regular solutions. The feature of the problems is a presence of new overdetermination conditions for the considered class of equations.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"2 1","pages":"62-74"},"PeriodicalIF":0.5000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Determination of parameters in telegraph equation\",\"authors\":\"A. I. Kozhanov, R. R. Safiullova\",\"doi\":\"10.13108/2017-9-1-62\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the solvability of the inverse problems on finding a solution u(x, t) and an unknown coefficient c for a telegraph equation utt −Δu+ cu = f(x, t). We prove the theorems on the existence of the regular solutions. The feature of the problems is a presence of new overdetermination conditions for the considered class of equations.\",\"PeriodicalId\":43644,\"journal\":{\"name\":\"Ufa Mathematical Journal\",\"volume\":\"2 1\",\"pages\":\"62-74\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2017-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ufa Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.13108/2017-9-1-62\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ufa Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13108/2017-9-1-62","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 8
摘要
研究了电报方程utt−Δu+ cu = f(x, t)的u(x, t)和未知系数c的反问题的可解性，证明了正则解的存在性定理。问题的特点是所考虑的一类方程存在新的超定条件。
We study the solvability of the inverse problems on finding a solution u(x, t) and an unknown coefficient c for a telegraph equation utt −Δu+ cu = f(x, t). We prove the theorems on the existence of the regular solutions. The feature of the problems is a presence of new overdetermination conditions for the considered class of equations.
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