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
Includes current open research problems
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
Includes current open research problems
Includes supplementary material: sn.pub/extras
A comprehensive deillegalscription 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.|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|
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 and Stationary Waves.- Integral Geometry and Tomography.- Hyperbolic Problems.- Inverse Parabolic Problems.- Some Numerical Methods.- Appendix: Functional Spaces.
This third edition expands upon the earlier edition by adding nearly 40 pages of new material reflecting the analytical and numerical progress in inverse problems in last 10 years. As in the second edition, the emphasis is on new ideas and methods rather than technical improvements. These new ideas include use of the stationary phase method in the two-dimensional elliptic problems and of multi frequenciestemporal data to improve stability and numerical resolution. There are also numerous corrections and improvements of the exposition throughout.
This book is intended for mathematicians working with partial differential equations and their applications, physicists, geophysicists, and financial, electrical, and mechanical engineers involved with nondestructive evaluation, seismic exploration, remote sensing, and various kinds of tomography.
Review 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)
This third edition expands upon the earlier edition by adding nearly 40 pages of new material reflecting the analytical and numerical progress in inverse problems in last 10 years. As in the second edition, the emphasis is on new ideas and methods rather than technical improvements. These new ideas include use of the stationary phase method in the two-dimensional elliptic problems and of multi frequenciestemporal data to improve stability and numerical resolution. There are also numerous corrections and improvements of the exposition throughout.
This book is intended for mathematicians working with partial differential equations and their applications, physicists, geophysicists, and financial, electrical, and mechanical engineers involved with nondestructive evaluation, seismic exploration, remote sensing, and various kinds of tomography.
Review 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)
"The book in its present third edition thus continues to serve as a valuable introduction and reference work on the contemporary analytical and numerical methods for treating inverse problems for PDE and it will guide its readers straight to forefront of current mathematical research questions in this field.” (Aleksandar Perovic, zbMATH, Vol. 1366.65087, 2017)
This third edition expands upon the earlier edition by adding nearly 40 pages of new material reflecting the analytical and numerical progress in inverse problems in last 10 years. As in the second edition, the emphasis is on new ideas and methods rather than technical improvements. These new ideas include use of the stationary phase method in the two-dimensional elliptic problems and of multi frequenciestemporal data to improve stability and numerical resolution. There are also numerous corrections and improvements of the exposition throughout.
This book is intended for mathematicians working with partial differential equations and their applications, physicists, geophysicists, and financial, electrical, and mechanical engineers involved with nondestructive evaluation, seismic exploration, remote sensing, and various kinds of tomography.
Review 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)
"The book in its present third edition thus continues to serve as a valuable introduction and reference work on the contemporary analytical and numerical methods for treating inverse problems for PDE and it will guide its readers straight to forefront of current mathematical research questions in this field." (Aleksandar Perovic, zbMATH, Vol. 1366.65087, 2017)
Inhaltsverzeichnis
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 and Stationary Waves.- Integral Geometry and Tomography.- Hyperbolic Problems.- Inverse Parabolic Problems.- Some Numerical Methods.- Appendix: Functional Spaces.
Klappentext
This third edition expands upon the earlier edition by adding nearly 40 pages of new material reflecting the analytical and numerical progress in inverse problems in last 10 years. As in the second edition, the emphasis is on new ideas and methods rather than technical improvements. These new ideas include use of the stationary phase method in the two-dimensional elliptic problems and of multi frequenciestemporal data to improve stability and numerical resolution. There are also numerous corrections and improvements of the exposition throughout.
This book is intended for mathematicians working with partial differential equations and their applications, physicists, geophysicists, and financial, electrical, and mechanical engineers involved with nondestructive evaluation, seismic exploration, remote sensing, and various kinds of tomography.
Review 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)
