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Introduction to Inverse Problems for Differential Equations

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Introduction to Inverse Problems for Differential Equations/ by Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov.
作者:	Hasanov Hasanoğlu, Alemdar.
其他作者:	Romanov, Vladimir G.
面頁冊數:	XVII, 515 p. 28 illus., 5 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Theoretical, Mathematical and Computational Physics. -
電子資源:	https://doi.org/10.1007/978-3-030-79427-9
ISBN:	9783030794279

Introduction to Inverse Problems for Differential Equations
Hasanov Hasanoğlu, Alemdar.

Introduction to Inverse Problems for Differential Equations[electronic resource] /by Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov. - 2nd ed. 2021. - XVII, 515 p. 28 illus., 5 illus. in color.online resource.

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 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. 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.

ISBN: 9783030794279

Standard No.: 10.1007/978-3-030-79427-9doiSubjects--Topical Terms:

768900
Theoretical, Mathematical and Computational Physics.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

Introduction to Inverse Problems for Differential Equations
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505 0 $a 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.
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