Inverse Problems In Partial Differential Equations
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Inverse Problems In Partial Differential Equations
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Author : David L. Colton
language : en
Publisher: SIAM
Release Date : 1990-01-01
Inverse Problems In Partial Differential Equations written by David L. Colton and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
Inverse Problems For Partial Differential Equations
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Author : Victor Isakov
language : en
Publisher: Springer
Release Date : 2017-02-24
Inverse Problems For Partial Differential Equations written by Victor Isakov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-24 with Mathematics categories.
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 For Fractional Partial Differential Equations
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Author : Barbara Kaltenbacher
language : en
Publisher: American Mathematical Society
Release Date : 2023-07-13
Inverse Problems For Fractional Partial Differential Equations written by Barbara Kaltenbacher and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-13 with Mathematics categories.
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.
Inverse Problems For Partial Differential Equations
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Author : Yurii Ya. Belov
language : en
Publisher: Walter de Gruyter
Release Date : 2012-02-14
Inverse Problems For Partial Differential Equations written by Yurii Ya. Belov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-14 with Mathematics categories.
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.
Introduction To Inverse Problems For Differential Equations
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Author : Alemdar Hasanov Hasanoğlu
language : en
Publisher: Springer Nature
Release Date : 2021-08-02
Introduction To Inverse Problems For Differential Equations written by Alemdar Hasanov Hasanoğlu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-02 with Mathematics categories.
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.
Advances In Inverse Problems For Partial Differential Equations
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Author : Dinh-Liem Nguyen
language : en
Publisher: American Mathematical Society
Release Date : 2023-04-12
Advances In Inverse Problems For Partial Differential Equations written by Dinh-Liem Nguyen and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-12 with Mathematics categories.
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.
Control And Inverse Problems For Partial Differential Equations
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Author : Bao Gang
language : en
Publisher: World Scientific
Release Date : 2019-04-08
Control And Inverse Problems For Partial Differential Equations written by Bao Gang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-08 with Mathematics categories.
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.
Inverse Problems For Partial Differential Equations
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Author : Yu. Ya Belov
language : en
Publisher: V.S.P. International Science
Release Date : 2002
Inverse Problems For Partial Differential Equations written by Yu. Ya Belov and has been published by V.S.P. International Science this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
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.
Partial Differential Equations And Inverse Problems
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Author : Carlos Conca
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Partial Differential Equations And Inverse Problems written by Carlos Conca and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Differential equations, Partial categories.
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.
Methods For Solving Inverse Problems In Mathematical Physics
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Author : Global Express Ltd. Co.
language : en
Publisher: CRC Press
Release Date : 2000-03-21
Methods For Solving Inverse Problems In Mathematical Physics written by Global Express Ltd. Co. and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-21 with Mathematics categories.
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, app