Introduction to Inverse Problems for Differential Equations

• Main Authors: Hasanov Hasanoğlu, Alemdar (Author), Romanov, Vladimir G. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Subjects: Mathematics.; Computer science > Mathematics.; Partial differential equations.; Computer mathematics.; Numerical analysis.; Physics.; Partial Differential Equations.; Computational Science and Engineering.; Numerical Analysis.; Mathematics of Computing.; Theoretical, Mathematical and Computational Physics.

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...

Table of 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.