Inverse Problems For Partial Differential Equations PDF Download
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Author | : Victor Isakov |
Publisher | : Springer Science & Business Media |
Total Pages | : 296 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1489900306 |
Download Inverse Problems for Partial Differential Equations Book in PDF, ePub and Kindle
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 |
Publisher | : Springer |
Total Pages | : 264 |
Release | : 2017-07-31 |
Genre | : Mathematics |
ISBN | : 331962797X |
Download Introduction to Inverse Problems for Differential Equations Book in PDF, ePub and Kindle
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 | : David L. Colton |
Publisher | : SIAM |
Total Pages | : 234 |
Release | : 1990-01-01 |
Genre | : Mathematics |
ISBN | : 9780898712520 |
Download Inverse Problems in Partial Differential Equations Book in PDF, ePub and Kindle
Author | : Barbara Kaltenbacher |
Publisher | : American Mathematical Society |
Total Pages | : 522 |
Release | : 2023-07-13 |
Genre | : Mathematics |
ISBN | : 1470472775 |
Download Inverse Problems for Fractional Partial Differential Equations Book in PDF, ePub and Kindle
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 | : Dinh-Liem Nguyen |
Publisher | : American Mathematical Society |
Total Pages | : 218 |
Release | : 2023-04-12 |
Genre | : Mathematics |
ISBN | : 1470469685 |
Download Advances in Inverse Problems for Partial Differential Equations Book in PDF, ePub and Kindle
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 | : Victor Isakov |
Publisher | : Springer |
Total Pages | : 406 |
Release | : 2018-07-21 |
Genre | : Mathematics |
ISBN | : 9783319847108 |
Download Inverse Problems for Partial Differential Equations Book in PDF, ePub and Kindle
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 | : Yurii Ya. Belov |
Publisher | : Walter de Gruyter |
Total Pages | : 220 |
Release | : 2012-02-14 |
Genre | : Mathematics |
ISBN | : 3110944634 |
Download Inverse Problems for Partial Differential Equations Book in PDF, ePub and Kindle
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 | : Chrisopher B. Croke |
Publisher | : Springer Science & Business Media |
Total Pages | : 334 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468493752 |
Download Geometric Methods in Inverse Problems and PDE Control Book in PDF, ePub and Kindle
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 | : Global Express Ltd. Co. |
Publisher | : CRC Press |
Total Pages | : 736 |
Release | : 2000-03-21 |
Genre | : Mathematics |
ISBN | : 9780824719876 |
Download Methods for Solving Inverse Problems in Mathematical Physics Book in PDF, ePub and Kindle
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.
Author | : Alemdar Hasanov Hasanoğlu |
Publisher | : Springer Nature |
Total Pages | : 521 |
Release | : 2021-08-02 |
Genre | : Mathematics |
ISBN | : 303079427X |
Download Introduction to Inverse Problems for Differential Equations Book in PDF, ePub and Kindle
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.