{"title":"Inverse Problem of Determining Two Coefficients of Lower-Order Terms in a Mixed Parabolic-Hyperbolic Equation","authors":"D. K. Durdiev","doi":"10.1134/s001226612401004x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Direct and inverse problems for a model equation of mixed parabolic-hyperbolic type are\nstudied. In the direct problem, we consider a Tricomi-type problem for this equation with a\nnoncharacteristic line of type change. The unknowns of the inverse problem are the variable\ncoefficients of the lower-order terms in the equation. To determine these coefficients, an integral\noverdetermination condition is specified relative to the solution defined in the parabolic part of the\ndomain, and in the hyperbolic part, conditions are specified on the characteristics: on one\ncharacteristic it is the value of the normal derivative and on the other, the value of the function\nitself. Theorems for the unique solvability of the posed problems in the sense of classical solution\nare proved.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s001226612401004x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Direct and inverse problems for a model equation of mixed parabolic-hyperbolic type are
studied. In the direct problem, we consider a Tricomi-type problem for this equation with a
noncharacteristic line of type change. The unknowns of the inverse problem are the variable
coefficients of the lower-order terms in the equation. To determine these coefficients, an integral
overdetermination condition is specified relative to the solution defined in the parabolic part of the
domain, and in the hyperbolic part, conditions are specified on the characteristics: on one
characteristic it is the value of the normal derivative and on the other, the value of the function
itself. Theorems for the unique solvability of the posed problems in the sense of classical solution
are proved.
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