Inverse Problems In Differential Equations PDF Download
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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 | : G. Anger |
Publisher | : Springer Science & Business Media |
Total Pages | : 266 |
Release | : 1990-06-30 |
Genre | : Science |
ISBN | : 9780306431647 |
Download Inverse Problems in Differential Equations Book in PDF, ePub and Kindle
Elucidates the fundamental mathematical structures of inverse problems, analyzing both the information content and the solution of some inverse problems in which the information content of the coefficients and the source term of a given differential equation is not too large. In order to be accessib
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 | : 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 | : Jaume Llibre |
Publisher | : Birkhäuser |
Total Pages | : 275 |
Release | : 2016-03-09 |
Genre | : Mathematics |
ISBN | : 3319263390 |
Download Inverse Problems in Ordinary Differential Equations and Applications Book in PDF, ePub and Kindle
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.
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 | : Charles W. Groetsch |
Publisher | : Springer Science & Business Media |
Total Pages | : 159 |
Release | : 2013-12-14 |
Genre | : Technology & Engineering |
ISBN | : 3322992020 |
Download Inverse Problems in the Mathematical Sciences Book in PDF, ePub and Kindle
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.
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.
Author | : M. M. Lavrentiev |
Publisher | : Springer |
Total Pages | : 65 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540364048 |
Download Multidimensional Inverse Problems for Differential Equations Book in PDF, ePub and Kindle
Author | : V. G. Romanov |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 248 |
Release | : 2018-11-05 |
Genre | : Mathematics |
ISBN | : 3110926016 |
Download Inverse Problems of Mathematical Physics Book in PDF, ePub and Kindle
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