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＜電子ブック＞
Introduction to Inverse Problems for Differential Equations / by Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov

版	2nd ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2021
本文言語	英語
大きさ	XVII, 515 p. 28 illus., 5 illus. in color : online resource
著者標目	*Hasanov Hasanoğlu, Alemdar author Romanov, Vladimir G author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Numerical analysis LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Mathematical physics FREE:Analysis FREE:Computational Science and Engineering FREE:Numerical Analysis FREE:Mathematics of Computing FREE:Theoretical, Mathematical and Computational Physics
一般注記	Introduction: Ill-Posedness of Inverse Problems for Differential and Integral Equations -- PART I. INTRODUCTION TO INVERSE PROBLEMS: 1. Functional Analysis Background of Ill-Posed Problems -- 2. Inverse Source Problems With Final Overdetermination -- PART II. INVERSE PROBLEMS FOR DIFFERENTIAL EQUATIONS: 3. Inverse Problems for Hyperbolic Equations -- 4. One-dimensional Inverse Problems for Electrodynamics Equations -- 5. Inverse Problems for Parabolic Equations -- 6. Inverse Problems for Elliptic Equations -- 7. Inverse Problems for the Stationary Transport Equations -- 8. The Inverse Kinematic Problem -- Appendix A: Invertibility of Linear Operators -- Appendix B: Some Estimates For One-dimensional Parabolic Equation -- Bibliography -- Index 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 andsource 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. For the second edition, the authors have added two new chapters focusing on real-world applications of inverse problems arising in wave and vibration phenomena. They have also revised the whole text of the first edition HTTP:URL=https://doi.org/10.1007/978-3-030-79427-9

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