Concurrent users
Unlimited
Authorized users
Authorized users
Document Delivery Supplied
Can lend chapters, not whole ebooks
Title
Introduction to inverse problems for differential equations / Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov.
Edition
Second edition.
ISBN
9783030794279 (electronic bk.)
303079427X (electronic bk.)
9783030794262
3030794261
Published
Cham : Springer, [2021]
Copyright
©2021
Language
English
Description
1 online resource : illustrations (some color)
Other Standard Identifiers
10.1007/978-3-030-79427-9 doi
Call Number
QA378.5 .H37 2021
Dewey Decimal Classification
515/.357
Summary
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 books 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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed August 16, 2021).
Available in Other Form
Print version: 9783030794262
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.
