Skip to main content
SpringerLink
Log in
Book cover

Inverse Problems for Partial Differential Equations

  • Book
  • © 2006

Overview

Authors:
  1. Victor Isakov

    1. Department of Mathematics and Statistics, The Wichita State University, Wichita, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Covers most important recent developments in inverse problems
  • Presented in a readable and informative manner
  • 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
  • Contains numerous exercises

Part of the book series: Applied Mathematical Sciences (AMS, volume 127)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Inverse Problems

    Pages 1-19

  3. Ill-Posed Problems and Regularization

    Pages 20-40

  4. Uniqueness and Stability in the Cauchy Problem

    Pages 41-88

  5. Elliptic Equations: Single Boundary Measurements

    Pages 89-126

  6. Elliptic Equations: Many Boundary Measurements

    Pages 127-172

  7. Scattering Problems

    Pages 173-191

  8. Integral Geometry and Tomography

    Pages 192-217

  9. Hyperbolic Problems

    Pages 218-254

  10. Inverse parabolic problems

    Pages 255-296

  11. Some Numerical Methods

    Pages 297-320

  12. Back Matter

    Pages 321-346
    Download chapter PDF
Back to top

Keywords

About this book

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

Reviews

From the reviews of the second edition:

"The first edition of this excellent book appeared in 1998 and became a standard reference for everyone interested in analysis and numerics of inverse problems in partial differential equations. … The second edition is considerably expanded and reflects important recent developments in the field … . Some of the research problems from the first edition have been solved … ." (Johannes Elschner, Zentralblatt MATH, Vol. 1092 (18), 2006)

Authors and Affiliations

  • Department of Mathematics and Statistics, The Wichita State University, Wichita, USA

    Victor Isakov

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation