Inverse Problems for Partial Differential Equations

Ön Kapak
Springer, 24 Şub 2017 - 406 sayfa
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In 8 years after publication of the ?rst version of this book, the rapidly progre- ing ?eld of inverse problems witnessed changes and new developments. Parts of the book were used at several universities, and many colleagues and students as well as myself observed several misprints and imprecisions. Some of the research problems from the ?rst edition have been solved. This edition serves the purposes of re?ecting these changes and making appropiate corrections. I hope that these additions and corrections resulted in not too many new errors and misprints. Chapters 1 and 2 contain only 2–3 pages of new material like in sections 1.5, 2.5. Chapter 3 is considerably expanded. In particular we give more convenient de?nition of pseudo-convexity for second order equations and included bou- ary terms in Carleman estimates (Theorem 3.2.1 ) and Counterexample 3.2.6. We give a new, shorter proof of Theorem 3.3.1 and new Theorems 3.3.7, 3.3.12, and Counterexample 3.3.9. We revised section 3.4, where a new short proof of exact observability inequality in given: proof of Theorem 3.4.1 and Theorems 3.4.3, 3.4.4, 3.4.8, 3.4.9 are new. Section 3.5 is new and it exposes recent progress on Carleman estimates, uniqueness and stability of the continuation for systems. In Chapter 4 we added to sections 4.5, 4.6 some new material on size evaluation of inclusionsandonsmallinclusions.Chapter5containsnewresultsonidenti?cation
 

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İçindekiler

Chapter 1 Inverse Problems
1
Chapter 2 IllPosed Problems and Regularization
23
Chapter 3 Uniqueness and Stability in the CauchyProblem
47
Single BoundaryMeasurements
104
Many BoundaryMeasurements
149
Chapter 6 Scattering Problems and Stationary Waves
211
Chapter 7 Integral Geometry and Tomography
240
Chapter 8 Hyperbolic Problems
269
Chapter 9 Inverse Parabolic Problems
309
Chapter 10 Some Numerical Methods
355
Appendix Function Spaces
381
References
384
Index
404
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