Introduction to inverse problems for differential equations / by Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov.

Format:

Book

Author/Creator:

Hasanov Hasanoğlu, Alemdar., Author.

Romanov, Vladimir G., Author.

Language:

English

Subjects (All):

Differential equations, Partial.

Computer science--Mathematics.

Computer science.

Numerical analysis.

Computer science—Mathematics.

Mathematical physics.

Partial Differential Equations.

Computational Science and Engineering.

Numerical Analysis.

Mathematics of Computing.

Theoretical, Mathematical and Computational Physics.

Local Subjects:

Partial Differential Equations.

Computational Science and Engineering.

Numerical Analysis.

Mathematics of Computing.

Theoretical, Mathematical and Computational Physics.

Physical Description:

1 online resource (261 pages)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

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 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.

Contents:

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.

Notes:

Includes bibliographical references and index.

ISBN:

3-319-62797-X