{"title":"On the Connections between Hyperbolic and Parabolic Inverse\nOne-Dimensional Discrete Problems","authors":"A. S. Mikhaylov, V. S. Mikhaylov","doi":"10.1134/S1990478924030116","DOIUrl":null,"url":null,"abstract":"<p> The boundary control method is applied to the solution of one-dimensional discrete\ninverse problems. The discrete counterparts of the operators used in the method (the control,\nresponse, and connecting operators) are defined. The relations between the operators\ncorresponding to the discrete wave equation and the discrete heat equation are established.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 3","pages":"503 - 515"},"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/S1990478924030116","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 boundary control method is applied to the solution of one-dimensional discrete
inverse problems. The discrete counterparts of the operators used in the method (the control,
response, and connecting operators) are defined. The relations between the operators
corresponding to the discrete wave equation and the discrete heat equation are established.
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.