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Author : David L. Colton,Richard E. Ewing,William Rundell,Society for Industrial and Applied Mathematics
Publisher : SIAM
Page : 234 pages
File Size : 54,9 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 0898712521
Author : Victor Isakov
Publisher : Springer
Page : 406 pages
File Size : 55,7 Mb
Release : 2017-02-24
Category : Mathematics
ISBN : 9783319516585
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.
Author : Barbara Kaltenbacher,William Rundell
Publisher : American Mathematical Society
Page : 522 pages
File Size : 43,8 Mb
Release : 2023-07-13
Category : Mathematics
ISBN : 9781470472771
As the title of the book indicates, this is primarily a book on partial differential equations (PDEs) with two definite slants: toward inverse problems and to the inclusion of fractional derivatives. The standard paradigm, or direct problem, is to take a PDE, including all coefficients and initial/boundary conditions, and to determine the solution. The inverse problem reverses this approach asking what information about coefficients of the model can be obtained from partial information on the solution. Answering this question requires knowledge of the underlying physical model, including the exact dependence on material parameters. The last feature of the approach taken by the authors is the inclusion of fractional derivatives. This is driven by direct physical applications: a fractional derivative model often allows greater adherence to physical observations than the traditional integer order case. The book also has an extensive historical section and the material that can be called "fractional calculus" and ordinary differential equations with fractional derivatives. This part is accessible to advanced undergraduates with basic knowledge on real and complex analysis. At the other end of the spectrum, lie nonlinear fractional PDEs that require a standard graduate level course on PDEs.
Author : Victor Isakov
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 52,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489900302
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.
Author : Alemdar Hasanov Hasanoğlu,Vladimir G. Romanov
Publisher : Springer
Page : 261 pages
File Size : 41,7 Mb
Release : 2017-07-31
Category : Mathematics
ISBN : 9783319627977
This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties.
Author : Yurii Ya. Belov
Publisher : Walter de Gruyter
Page : 220 pages
File Size : 41,7 Mb
Release : 2012-02-14
Category : Mathematics
ISBN : 9783110944631
This monograph is devoted to identification problems of coefficients in equations of mathematical physics. It invesitgates the existence and uniqueness of the solutions for identification coefficient problems in parabolic and hyperbolic equations and equation systems of composite type. The problems are studied with the Cauchy data and equations in which the Fourier transform with respect to the chosen variable is supposed to occur. Differential properties of the solutions for the original direct problems and their behavior under great values of time are studied on the basis of solution properties for direct problems. The identification problems with one or two unknown coefficients are also investigated. For initial boundary value conditions linear and nonlinear parabolic equations are studied.
Author : Dinh-Liem Nguyen,Loc Hoang Nguyen,Thi-Phong Nguyen
Publisher : American Mathematical Society
Page : 218 pages
File Size : 53,5 Mb
Release : 2023-04-12
Category : Mathematics
ISBN : 9781470469689
This volume contains the proceedings of two AMS Special Sessions “Recent Developments on Analysis and Computation for Inverse Problems for PDEs,” virtually held on March 13–14, 2021, and “Recent Advances in Inverse Problems for Partial Differential Equations,” virtually held on October 23–24, 2021. The papers in this volume focus on new results on numerical methods for various inverse problems arising in electrical impedance tomography, inverse scattering in radar and optics problems, reconstruction of initial conditions, control of acoustic fields, and stock price forecasting. The authors studied iterative and non-iterative approaches such as optimization-based, globally convergent, sampling, and machine learning-based methods. The volume provides an interesting source on advances in computational inverse problems for partial differential equations.
Author : Bao Gang,Coron Jean-michel,Li Ta-tsien
Publisher : World Scientific
Page : 264 pages
File Size : 40,7 Mb
Release : 2019-04-08
Category : Mathematics
ISBN : 9789813276161
This book is a collection of lecture notes for the LIASFMA Hangzhou Autumn School on 'Control and Inverse Problems for Partial Differential Equations' which was held during October 17-22, 2016 at Zhejiang University, Hangzhou, China. This autumn school is one of the activities organized by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA). Established jointly by eight institutions in China and France in 2014, LIASFMA aims at providing a platform for many leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in broad areas of applied mathematics.The book provides the readers with a unique and valuable opportunity to learn from and communicate with leading experts in control and inverse problems. And the readers are exposed not only to the basic theories and methods but also to the forefront of research directions in both fields.
Author : Alemdar Hasanov Hasanoğlu,Vladimir G. Romanov
Publisher : Springer Nature
Page : 521 pages
File Size : 51,5 Mb
Release : 2021-08-02
Category : Mathematics
ISBN : 9783030794279
This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties. For the second edition, the authors have added two new chapters focusing on real-world applications of inverse problems arising in wave and vibration phenomena. They have also revised the whole text of the first edition.
Author : Chrisopher B. Croke,Gunther Uhlmann,Irena Lasiecka,Michael Vogelius
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493757
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.
Author : Carlos Conca
Publisher : American Mathematical Soc.
Page : 426 pages
File Size : 41,5 Mb
Release : 2004
Category : Differential equations, Partial
ISBN : 9780821834480
This proceedings volume is a collection of articles from the Pan-American Advanced Studies Institute on partial differential equations, nonlinear analysis and inverse problems held in Santiago (Chile). Interactions among partial differential equations, nonlinear analysis, and inverse problems have produced remarkable developments over the last couple of decades. This volume contains survey articles reflecting the work of leading experts who presented minicourses at the event. Contributors include J. Busca, Y. Capdeboscq, M.S. Vogelius, F. A. Grunbaum, L. F. Matusevich, M. de Hoop, and P. Kuchment. The volume is suitable for graduate students and researchers interested in partial differential equations and their applications in nonlinear analysis and inverse problems.
Author : Yu. Ya Belov
Publisher : V.S.P. International Science
Page : 211 pages
File Size : 45,6 Mb
Release : 2002
Category : Mathematics
ISBN : 9067643580
This monograph is devoted to identification problems of coefficients in equations of mathematical physics. It invesitgates the existence and uniqueness of the solutions for identification coefficient problems in parabolic and hyperbolic equations and equation systems of composite type. The problems are studied with the Cauchy data and equations in which the Fourier transform with respect to the chosen variable is supposed to occur. Differential properties of the solutions for the original direct problems and their behavior under great values of time are studied on the basis of solution properties for direct problems. The identification problems with one or two unknown coefficients are also investigated. For initial boundary value conditions linear and nonlinear parabolic equations are studied.
Author : G. Anger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 256 pages
File Size : 52,5 Mb
Release : 1990-12-31
Category : Mathematics
ISBN : 9783112707173
No detailed description available for "Inverse Problems in Differential Equations".
Author : Andreas Kirsch
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 42,6 Mb
Release : 2011-03-24
Category : Mathematics
ISBN : 9781441984746
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.
Author : Jaume Llibre,Rafael Ramírez
Publisher : Birkhäuser
Page : 266 pages
File Size : 41,9 Mb
Release : 2016-03-09
Category : Mathematics
ISBN : 9783319263397
This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in R^N which have a given set of partial integrals or first integrals. The results obtained are applied first to planar polynomial differential systems with a given set of such integrals, second to solve the 16th Hilbert problem restricted to generic algebraic limit cycles, third for solving the inverse problem for constrained Lagrangian and Hamiltonian mechanical systems, fourth for studying the integrability of a constrained rigid body. Finally the authors conclude with an analysis on nonholonomic mechanics, a generalization of the Hamiltonian principle, and the statement an solution of the inverse problem in vakonomic mechanics.
