Ill Posed Problems Of Mathematical Physics And Analysis
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Ill Posed Problems Of Mathematical Physics And Analysis
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Author : Mikhail Mikha_lovich Lavrent_ev
language : en
Publisher: American Mathematical Soc.
Release Date : 1986-12-31
Ill Posed Problems Of Mathematical Physics And Analysis written by Mikhail Mikha_lovich Lavrent_ev 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 1986-12-31 with Mathematics categories.
Physical formulations leading to ill-posed problems Basic concepts of the theory of ill-posed problems Analytic continuation Boundary value problems for differential equations Volterra equations Integral geometry Multidimensional inverse problems for linear differential equations
Ill Posed Problems Of Mathematical Physics And Analysis
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Author : Mikhail Mikhaĭlovich Lavrentʹev
language : en
Publisher: Providence, R.I. : American Mathematical Society
Release Date : 1986
Ill Posed Problems Of Mathematical Physics And Analysis written by Mikhail Mikhaĭlovich Lavrentʹev and has been published by Providence, R.I. : American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Ill Posed Problems Of Mathematical Physics And Analysis
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Author : Mikhail Mikhaĭlovich Lavrentʹev
language : en
Publisher:
Release Date : 1986
Ill Posed Problems Of Mathematical Physics And Analysis written by Mikhail Mikhaĭlovich Lavrentʹev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Boundary value problems categories.
Ill Posed And Non Classical Problems Of Mathematical Physics And Analysis
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Author : Mikhail M. Lavrent'ev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-07-24
Ill Posed And Non Classical Problems Of Mathematical Physics And Analysis written by Mikhail M. Lavrent'ev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-24 with Mathematics categories.
These proceedings of the international Conference "Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis", held at the Samarkand State University, Uzbekistan in September 2000 bring together fundamental research articles in the major areas of the numerated fields of analysis and mathematical physics. The book covers the following topics: theory of ill-posed problems inverse problems for differential equations boundary value problems for equations of mixed type integral geometry mathematical modelling and numerical methods in natural sciences
Ill Posed Problems Of Mathematical Physics And Analysis
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Author : Mikhail Mikhailovich Lavrent'ev
language : en
Publisher:
Release Date : 1986
Ill Posed Problems Of Mathematical Physics And Analysis written by Mikhail Mikhailovich Lavrent'ev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Ill Posed And Non Classical Problems Of Mathematical Physics And Analysis
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Author : Mikhail M. Lavrent'ev
language : en
Publisher: V.S.P. International Science
Release Date : 2003
Ill Posed And Non Classical Problems Of Mathematical Physics And Analysis written by Mikhail M. Lavrent'ev 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 2003 with Mathematics categories.
These proceedings of the international Conference "Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis", held at the Samarkand State University, Uzbekistan in September 2000 bring together fundamental research articles in the major areas of the numerated fields of analysis and mathematical physics. The book covers the following topics: theory of ill-posed problems inverse problems for differential equations boundary value problems for equations of mixed type integral geometry mathematical modelling and numerical methods in natural sciences
Inverse And Ill Posed Problems
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Author : Sergey I. Kabanikhin
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-23
Inverse And Ill Posed Problems written by Sergey I. Kabanikhin 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 2011-12-23 with Mathematics categories.
The theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a subject in which its creator takes a keen interest. The concept of ill-posed problems was introduced by Hadamard with the comment that these problems are physically meaningless and not worthy of the attention of serious researchers. Despite Hadamard's pessimistic forecasts, however, his unloved "child" has turned into a powerful theory whose results are used in many fields of pure and applied mathematics. What is the secret of its success? The answer is clear. Ill-posed problems occur everywhere and it is unreasonable to ignore them. Unlike ill-posed problems, inverse problems have no strict mathematical definition. In general, they can be described as the task of recovering a part of the data of a corresponding direct (well-posed) problem from information about its solution. Inverse problems were first encountered in practice and are mostly ill-posed. The urgent need for their solution, especially in geological exploration and medical diagnostics, has given powerful impetus to the development of the theory of ill-posed problems. Nowadays, the terms "inverse problem" and "ill-posed problem" are inextricably linked to each other. Inverse and ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material. This book is the first small step in that direction. We propose a classification of inverse problems according to the type of equation, unknowns and additional information. We consider specific problems from a single position and indicate relationships between them. The problems relate to different areas of mathematics, such as linear algebra, theory of integral equations, integral geometry, spectral theory and mathematical physics. We give examples of applied problems that can be studied using the techniques we describe. This book was conceived as a textbook on the foundations of the theory of inverse and ill-posed problems for university students. The author's intention was to explain this complex material in the most accessible way possible. The monograph is aimed primarily at those who are just beginning to get to grips with inverse and ill-posed problems but we hope that it will be useful to anyone who is interested in the subject.
Optimal Methods For Ill Posed Problems
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Author : Vitalii P. Tanana
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-03-19
Optimal Methods For Ill Posed Problems written by Vitalii P. Tanana and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with Mathematics categories.
The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. Contents Modulus of continuity of the inverse operator and methods for solving ill-posed problems Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind Tikhonov regularization method Projection-regularization method Inverse heat exchange problems
Regularization Algorithms For Ill Posed Problems
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Author : Anatoly B. Bakushinsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05
Regularization Algorithms For Ill Posed Problems written by Anatoly B. Bakushinsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.
This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems
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.