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Inverse Problems for Partial Differential Equations

Inverse Problems for Partial Differential Equations Author Victor Isakov
ISBN-10 9783319516585
Release 2017-03-25
Pages 408
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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 in Partial Differential Equations

Inverse Problems in Partial Differential Equations Author David L. Colton
ISBN-10 0898712521
Release 1990-01-01
Pages 214
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Inverse Problems in Partial Differential Equations has been writing in one form or another for most of life. You can find so many inspiration from Inverse Problems in Partial Differential Equations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Inverse Problems in Partial Differential Equations book for free.

Modern Aspects of the Theory of Partial Differential Equations

Modern Aspects of the Theory of Partial Differential Equations Author Michael V. Ruzhansky
ISBN-10 303480069X
Release 2011-05-04
Pages 368
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The book provides a quick overview of a wide range of active research areas in partial differential equations. The book can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions from authors from a large variety of countries on different aspects of partial differential equations, such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches.

Phase Space Analysis of Partial Differential Equations

Phase Space Analysis of Partial Differential Equations Author Antonio Bove
ISBN-10 0817645217
Release 2007-12-28
Pages 343
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This collection of original articles and surveys treats linear and nonlinear aspects of the theory of partial differential equations. Phase space analysis methods, also known as microlocal analysis, have yielded striking results over the past years and have become one of the main tools of investigation. Equally important is their role in many applications to physics, for example, in quantum and spectral theory. Contributors: H. Bahouri, M. Baouendi, E. Bernardi, M. Bony, A. Bove, N. Burq, J.-Y. Chemin, F. Colombini, T. Colin, P. Cordaro, G. Eskin, X. Fu, N. Hanges, G. Métivier, P. Michor, T. Nishitani, A. Parmeggiani,L. Pernazza, V. Petkov, F. Planchon, M. Prizzi, D. Del Santo, D. Tartakof, D. Tataru, F. Treves, C.-J. Xu, X. Zhang, E. Zuazua

Inverse Problems and Applications

Inverse Problems and Applications Author Plamen Stefanov
ISBN-10 9781470410797
Release 2014-05-05
Pages 309
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This volume contains the proceedings of two conferences on Inverse Problems and Applications, held in 2012, to celebrate the work of Gunther Uhlmann. The first conference was held at the University of California, Irvine, from June 18-22, 2012, and the second was held at Zhejiang University, Hangzhou, China, from September 17-21, 2012. The topics covered include inverse problems in medical imaging, scattering theory, geometry and image processing, and the mathematical theory of cloaking, as well as methods related to inverse problems.

Inverse Problems in the Mathematical Sciences

Inverse Problems in the Mathematical Sciences Author Charles W. Groetsch
ISBN-10 9783322992024
Release 2013-12-14
Pages 154
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Inverse problems are immensely important in modern science and technology. However, the broad mathematical issues raised by inverse problems receive scant attention in the university curriculum. This book aims to remedy this state of affairs by supplying an accessible introduction, at a modest mathematical level, to the alluring field of inverse problems. Many models of inverse problems from science and engineering are dealt with and nearly a hundred exercises, of varying difficulty, involving mathematical analysis, numerical treatment, or modelling of inverse problems, are provided. The main themes of the book are: causation problem modeled as integral equations; model identification problems, posed as coefficient determination problems in differential equations; the functional analytic framework for inverse problems; and a survey of the principal numerical methods for inverse problems. An extensive annotated bibliography furnishes leads on the history of inverse problems and a guide to the frontiers of current research.

Methods for Solving Inverse Problems in Mathematical Physics

Methods for Solving Inverse Problems in Mathematical Physics Author Global Express Ltd. Co.
ISBN-10 0824719875
Release 2000-03-21
Pages 744
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Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.

Inverse Problems for Electrical Networks

Inverse Problems for Electrical Networks Author Edward B. Curtis
ISBN-10 9810241747
Release 2000
Pages 184
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Annotation This book is a very timely exposition of part of an important subject which goes under the general name of "inverse problems". The analogous problem for continuous media has been very much studied, with a great deal of difficult mathematics involved, especially partial differential equations. Some of the researchers working on the inverse conductivity problem for continuous media (the problem of recovering the conductivity inside from measurements on the outside) have taken an interest in the authors' analysis of this similar problem for resistor networks. The authors' treatment of inverse problems for electrical networks is at a fairly elementary level. It is accessible to advanced undergraduates, and mathematics students at the graduate level. The topics are of interest to mathematicians working on inverse problems, and possibly to electrical engineers. A few techniques from other areas of mathematics have been brought together in the treatment. It is this amalgamation of such topics as graphtheory, medial graphs and matrix algebra, as well as the analogy to inverse problems for partial differential equations, that makes the book both original and interesting.

Geometric Methods in Inverse Problems and PDE Control

Geometric Methods in Inverse Problems and PDE Control Author Chrisopher B. Croke
ISBN-10 9781468493757
Release 2012-12-06
Pages 330
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This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title. We would like to thank Christopher B. Croke (University of Penn sylva nia), Irena Lasiecka (University of Virginia), Gunther Uhlmann (University of Washington), and Michael S. Vogelius (Rutgers University) for their ex cellent work as organizers of the two-week summer workshop and for editing the volume. We also take this opportunity to thank the National Science Founda tion for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a selected number of articles based on lectures delivered at the IMA 2001 Summer Program on "Geometric Methods in Inverse Problems and PDE Control. " The focus of this program was some common techniques used in the study of inverse coefficient problems and control problems for partial differential equations, with particular emphasis on their strong relation to fundamental problems of geometry. Inverse coef ficient problems for partial differential equations arise in many application areas, for instance in medical imaging, nondestructive testing, and geophys ical prospecting. Control problems involving partial differential equations may arise from the need to optimize a given performance criterion, e. g. , to dampen out undesirable vibrations of a structure , or more generally, to obtain a prescribed behaviour of the dynamics.

Partial Differential Equations

Partial Differential Equations Author David Colton
ISBN-10 9780486138435
Release 2012-06-14
Pages 320
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This text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Features coverage of integral equations and basic scattering theory. Includes exercises, many with answers. 1988 edition.

Inverse Boundary Spectral Problems

Inverse Boundary Spectral Problems Author Alexander Kachalov
ISBN-10 9781420036220
Release 2001-07-30
Pages 260
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Inverse boundary problems are a rapidly developing area of applied mathematics with applications throughout physics and the engineering sciences. However, the mathematical theory of inverse problems remains incomplete and needs further development to aid in the solution of many important practical problems. Inverse Boundary Spectral Problems develop a rigorous theory for solving several types of inverse problems exactly. In it, the authors consider the following: "Can the unknown coefficients of an elliptic partial differential equation be determined from the eigenvalues and the boundary values of the eigenfunctions?" Along with this problem, many inverse problems for heat and wave equations are solved. The authors approach inverse problems in a coordinate invariant way, that is, by applying ideas drawn from differential geometry. To solve them, they apply methods of Riemannian geometry, modern control theory, and the theory of localized wave packets, also known as Gaussian beams. The treatment includes the relevant background of each of these areas. Although the theory of inverse boundary spectral problems has been in development for at least 10 years, until now the literature has been scattered throughout various journals. This self-contained monograph summarizes the relevant concepts and the techniques useful for dealing with them.

An Introduction to the Mathematical Theory of Inverse Problems

An Introduction to the Mathematical Theory of Inverse Problems Author Andreas Kirsch
ISBN-10 1441984747
Release 2011-03-24
Pages 310
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This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples. The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. The choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students. Basic knowledge of real analysis is assumed. In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph as Chapter 5 while the chapter on inverse scattering theory is now Chapter 6.The main changes of this second edition compared to the first edition concern only Chapters 5 and 6 and the Appendix A. Chapter 5 introduces the reader to the inverse problem of electrical impedance tomography.

Linear Inverse Problems and Tikhonov Regularization

Linear Inverse Problems and Tikhonov Regularization Author Mark Gockenbach
ISBN-10 9780883851418
Release 2016-11-24
Pages 333
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Inverse problems occur frequently in science and technology, whenever we need to infer causes from effects that we can measure. Mathematically, they are difficult problems because they are unstable: small bits of noise in the measurement can completely throw off the solution. Nevertheless, there are methods for finding good approximate solutions. Linear Inverse Problems and Tikhonov Regularization examines one such method: Tikhonov regularization for linear inverse problems defined on Hilbert spaces. This is a clear example of the power of applying deep mathematical theory to solve practical problems. Beginning with a basic analysis of Tikhonov regularization, this book introduces the singular value expansion for compact operators, and uses it to explain why and how the method works. Tikhonov regularization with seminorms is also analyzed, which requires introducing densely defined unbounded operators and their basic properties. Some of the relevant background is included in appendices, making the book accessible to a wide range of readers.

Modeling and Inverse Problems in Imaging Analysis

Modeling and Inverse Problems in Imaging Analysis Author Bernard Chalmond
ISBN-10 038795547X
Release 2003-01-14
Pages 309
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More mathematics have been taking part in the development of digital image processing as a science, and the contributions are reflected in the increasingly important role modeling has played solving complex problems. This book is mostly concerned with energy-based models. Through concrete image analysis problems, the author develops consistent modeling, a know-how generally hidden in the proposed solutions. The book is divided into three main parts. The first two parts describe the theory behind the applications that are presented in the third part. These materials include splines (variational approach, regression spline, spline in high dimension) and random fields (Markovian field, parametric estimation, stochastic and deterministic optimization, continuous Gaussian field). Most of these applications come from industrial projects in which the author was involved in robot vision and radiography: tracking 3-D lines, radiographic image processing, 3-D reconstruction and tomography, matching and deformation learning. Numerous graphical illustrations accompany the text showing the performance of the proposed models. This book will be useful to researchers and graduate students in mathematics, physics, computer science, and engineering.

Improperly Posed Problems in Partial Differential Equations

Improperly Posed Problems in Partial Differential Equations Author L. E. Payne
ISBN-10 9780898710199
Release 1975-06-01
Pages 76
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A discussion of improperly posed Cauchy problems in partial differential equations

Partial Differential Equations I

Partial Differential Equations I Author Michael Eugene Taylor
ISBN-10 0387946535
Release 1996-01-01
Pages 563
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This book is intended to be a comprehensive introduction to the subject of partial differential equations. It should be useful to graduate students at all levels beyond that of a basic course in measure theory. It should also be of interest to professional mathematicians in analysis, mathematical physics, and differential geometry. This work will be divided into three volumes, the first of which focuses on the theory of ordinary differential equations and a survey of basic linear PDEs.

Perspectives in Mathematical Sciences

Perspectives in Mathematical Sciences Author Yisong Yang
ISBN-10 9789814289313
Release 2010
Pages 354
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Mathematical sciences have been playing an increasingly important role in modern society. They are in high demand for investigating complex problems in physical science, environmental and geophysical sciences, materials science, life science and chemical sciences. This is a review volume on some timely and interesting topics in applied mathematical sciences. It reviews new developments and presents some future research directions in these topics. The chapters are written by reknowned experts in these fields. The volume is written with a wide audience in mind and hence will be accessible to graduate students, junior researchers and other professionals who are interested in the subject. The contributions of Professor Youzhong Guo, a leading expert in these areas, will be celebrated. An entire chapter will be devoted to his achievements. The underlying theme that binds the various chapters seamlessly is a set of dedicated ideas and techniques from partial differential equations and dynamical systems.