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Introduction to Inverse Problems for Differential Equations

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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 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)

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