Introduction to Inverse Problems for Differential Equations

“This monograph provides a well-written, easy-to-read, and basically self-contained survey on a wide range of inverse problems related with initial-boundary problems for partial deferential equations. It addresses many relevant topics in the theory of such problems, with a focus on existence, uniqueness and stability of inverse coefficient and source problems. … The text can be used for self-study and will be of interest to experts in the field as well as graduate students.” (Boris Rubin, zbMATH 1385.65053, 2018)“This book is an important contribution to the theory of inverse problems. It gives a complete picture of inverse problems and their applications. … It is a good research monograph for people working on inverse problems and related issues; a useful state-of-the-art reference guide for researchers and students; and a fine textbook for graduate students in mathematics and engineering.” (Srinivasan Natesan, Computing Reviews, September, 2018)

• 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.