{"title":"Inverse Problems of Finding a Source\nin the Heat Equation from a Nonlocal Observation","authors":"K. B. Sabitov","doi":"10.1134/S1990478924030141","DOIUrl":null,"url":null,"abstract":"<p> The article presents the statement of inverse problems of finding the right-hand side of the\nheat equation from an additional integral condition and justifies their Hadamard well-posedness in\nthe class of regular solutions. The uniqueness of solutions of the problems is proved on the basis of\nintegral identities. The solutions of the problems are constructed explicitly using separation of\nvariables and the integral equation method.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 3","pages":"536 - 547"},"PeriodicalIF":0.5800,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924030141","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
The article presents the statement of inverse problems of finding the right-hand side of the
heat equation from an additional integral condition and justifies their Hadamard well-posedness in
the class of regular solutions. The uniqueness of solutions of the problems is proved on the basis of
integral identities. The solutions of the problems are constructed explicitly using separation of
variables and the integral equation method.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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