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Autor: Victor Isakov
ISBN-13: 9780387321837
Einband: eBook
Seiten: 346
Sprache: Englisch
eBook Typ: PDF
eBook Format: eBook
Kopierschutz: Adobe DRM [Hard-DRM]
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Inverse Problems for Partial Differential Equations

127, Applied Mathematical Sciences
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A comprehensive description of the current theoretical and numerical aspects of inverse problems in partial differential equations. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurement. By presenting the data in a readable and informative manner, the book introduces both scientific and engineering researchers as well as graduate students to the significant work done in this area in recent years, relating it to broader themes in mathematical analysis.
Inverse Problems.- Ill-Posed Problems and Regularization.- Uniqueness and Stability in the Cauchy Problem.- Elliptic Equations: Single Boundary Measurements.- Elliptic Equations: Many Boundary Measurements.- Scattering Problems.- Integral Geometry and Tomography.- Hyperbolic Problems.- Inverse parabolic problems.- Some Numerical Methods.
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 23 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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Autor: Victor Isakov
ISBN-13:: 9780387321837
ISBN: 0387321837
Erscheinungsjahr: 23.12.2005
Verlag: Springer New York
Seiten: 346
Sprache: Englisch
Auflage 2, 2nd ed. 2006
Sonstiges: Ebook, Since the first publication of this book, the rapidly progressing field of inverse problems witnessed changes and new developments. This book reflects these changes and describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. Currently, there are hundreds of publications containing new and interesting results on the topic of inverse problems. This book successfully collects and presents many of them in a readable and informa