Inverse Problems for Partial Differential EquationsSpringer, 24 Şub 2017 - 406 sayfa 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 |
İçindekiler
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 |
404 | |
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additional analytic applied assume assumptions boundary condition boundary data boundary value problem bounded Cauchy problem coefficients conclude condition conductivity consider constant contained continuous convergence convex Corollary corresponding defined definition depend derivatives describe differential equation direct Dirichlet data Dirichlet problem Dirichlet-to-Neumann map domain elliptic equations equality estimate example Exercise existence final formula function give given harmonic hence hyperbolic implies important inequality initial integral interesting introduce inverse problem known lateral boundary Lemma linear Lipschitz measurements method norm numerical observe obtain operator origin particular plane positive potential principle proof proof of Theorem prove refer regularization relation replace respect satisfies scattering side similar smooth solution solves space stability estimate term Theorem theory tion transform uniquely determines wave zero