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Introduction to inverse problems for differential equations

This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PD...

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Detalles Bibliográficos
Autores principales: Hasanov Hasanoğlu, Alemdar, Romanov, Vladimir G
Lenguaje:eng
Publicado: Springer 2017
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-62797-7
http://cds.cern.ch/record/2276956
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author Hasanov Hasanoğlu, Alemdar
Romanov, Vladimir G
author_facet Hasanov Hasanoğlu, Alemdar
Romanov, Vladimir G
author_sort Hasanov Hasanoğlu, Alemdar
collection CERN
description This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties.
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spelling cern-22769562021-04-21T19:08:24Zdoi:10.1007/978-3-319-62797-7http://cds.cern.ch/record/2276956engHasanov Hasanoğlu, AlemdarRomanov, Vladimir GIntroduction to inverse problems for differential equationsMathematical Physics and MathematicsThis book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties.Springeroai:cds.cern.ch:22769562017
spellingShingle Mathematical Physics and Mathematics
Hasanov Hasanoğlu, Alemdar
Romanov, Vladimir G
Introduction to inverse problems for differential equations
title Introduction to inverse problems for differential equations
title_full Introduction to inverse problems for differential equations
title_fullStr Introduction to inverse problems for differential equations
title_full_unstemmed Introduction to inverse problems for differential equations
title_short Introduction to inverse problems for differential equations
title_sort introduction to inverse problems for differential equations
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-62797-7
http://cds.cern.ch/record/2276956
work_keys_str_mv AT hasanovhasanoglualemdar introductiontoinverseproblemsfordifferentialequations
AT romanovvladimirg introductiontoinverseproblemsfordifferentialequations