Investigation Methods For Inverse Problems
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Introduction To Inverse Problems For Differential Equations
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Author : Alemdar Hasanov Hasanoğlu
language : en
Publisher: Springer
Release Date : 2017-07-31
Introduction To Inverse Problems For Differential Equations written by Alemdar Hasanov Hasanoğlu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-31 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.
Inverse Problems
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Author : Alexander G. Ramm
language : en
Publisher: Springer
Release Date : 2004-12-16
Inverse Problems written by Alexander G. Ramm and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-16 with Computers categories.
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
Inverse Problems Of Mathematical Physics
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Author :
language : en
Publisher: VSP
Release Date : 2003
Inverse Problems Of Mathematical Physics written by and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Thismonograph deals with the theory of inverse problems of mathematical physics andapplications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.
Investigation Methods For Inverse Problems
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Author : Vladimir G. Romanov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-10-10
Investigation Methods For Inverse Problems written by Vladimir G. Romanov 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 2014-10-10 with Mathematics categories.
This monograph deals with some inverse problems of mathematical physics. It introduces new methods for studying inverse problems and gives obtained results, which are related to the conditional well posedness of the problems. The main focus lies on time-domain inverse problems for hyperbolic equations and the kinetic transport equation.
Operator Theory And Ill Posed Problems
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Author : Mikhail M. Lavrent'ev
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22
Operator Theory And Ill Posed Problems written by Mikhail M. Lavrent'ev 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 2011-12-22 with Mathematics categories.
This book consists of three major parts. The first two parts deal with general mathematical concepts and certain areas of operator theory. The third part is devoted to ill-posed problems. It can be read independently of the first two parts and presents a good example of applying the methods of calculus and functional analysis. The first part "Basic Concepts" briefly introduces the language of set theory and concepts of abstract, linear and multilinear algebra. Also introduced are the language of topology and fundamental concepts of calculus: the limit, the differential, and the integral. A special section is devoted to analysis on manifolds. The second part "Operators" describes the most important function spaces and operator classes for both linear and nonlinear operators. Different kinds of generalized functions and their transformations are considered. Elements of the theory of linear operators are presented. Spectral theory is given a special focus. The third part "Ill-Posed Problems" is devoted to problems of mathematical physics, integral and operator equations, evolution equations and problems of integral geometry. It also deals with problems of analytic continuation. Detailed coverage of the subjects and numerous examples and exercises make it possible to use the book as a textbook on some areas of calculus and functional analysis. It can also be used as a reference textbook because of the extensive scope and detailed references with comments.
Counterexamples In Optimal Control Theory
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Author : Semen Ya. Serovaiskii
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-01
Counterexamples In Optimal Control Theory written by Semen Ya. Serovaiskii 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 2011-12-01 with Mathematics categories.
This monograph deals with cases where optimal control either does not exist or is not unique, cases where optimality conditions are insufficient of degenerate, or where extremum problems in the sense of Tikhonov and Hadamard are ill-posed, and other situations. A formal application of classical optimisation methods in such cases either leads to wrong results or has no effect. The detailed analysis of these examples should provide a better understanding of the modern theory of optimal control and the practical difficulties of solving extremum problems.
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
Characterisation Of Bio Particles From Light Scattering
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Author : Valeri P. Maltsev
language : en
Publisher: Walter de Gruyter
Release Date : 2013-03-01
Characterisation Of Bio Particles From Light Scattering written by Valeri P. Maltsev 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 2013-03-01 with Mathematics categories.
The primary aim of this monograph is to provide a systematic state-of-the-art summary of the light scattering of bioparticles, including a brief consideration of analytical and numerical methods for computing electromagnetic scattering by single particles, a detailed discussion of the instrumental approach used in measurement of light scattering, an analysis of the methods used in solution of the inverse light scattering problem, and an introduction of the results dealing with practical analysis of biosamples. Considering the widespread need for this information in optics, remote sensing, engineering, medicine, and biology, the book is useful to many graduate students, scientists, and engineers working on various aspects of electromagnetic scattering and its applications.
Well Posed Ill Posed And Intermediate Problems With Applications
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Author : Petrov Yuri P.
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22
Well Posed Ill Posed And Intermediate Problems With Applications written by Petrov Yuri P. 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 2011-12-22 with Mathematics categories.
This book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples.
Poorly Visible Media In X Ray Tomography
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Author : V. G. Nazarov
language : en
Publisher: VSP
Release Date : 2002-01-01
Poorly Visible Media In X Ray Tomography written by V. G. Nazarov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Science categories.
The tomography problem considered in this volume of the Inverse and Ill-Posed Problems Series consists of finding an essential part of information about the internal structure of an unknown medium. More particularly, the contact boundaries between various materials in the medium are sought. This investigation is implemented by studying an appropriate mathematical model, which is represented as a transport equation (linear Boltzmann's equation) together with certain boundary conditions. Both theoretical and numerical methods have been used and the results consist of proved theorems, computer testing of the corresponding algorithms, together with a number of tables. This book may be considered as a continuation and application of Transport Equation and Tomography by D.S. Anikonov, A.E. Kovtanyuk and I.V. Prokhorov, previously published in this series.