Direct Methods Of Solving Multidimensional Inverse Hyperbolic Problems

DOWNLOAD

Download Direct Methods Of Solving Multidimensional Inverse Hyperbolic Problems PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Direct Methods Of Solving Multidimensional Inverse Hyperbolic Problems book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Direct Methods Of Solving Multidimensional Inverse Hyperbolic Problems

DOWNLOAD
Author : Sergey I. Kabanikhin
language : en
Publisher: Walter de Gruyter
Release Date : 2013-04-09

Direct Methods Of Solving Multidimensional Inverse Hyperbolic 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 2013-04-09 with Mathematics categories.

The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection method and prove theorems of convergence, conditional stability, and other properties of the mentioned methods.

Direct Methods Of Solving Multidimensional Inverse Hyperbolic Problems

DOWNLOAD
Author : S. I. Kabanikhin
language : en
Publisher: Walter de Gruyter
Release Date : 2004

Direct Methods Of Solving Multidimensional Inverse Hyperbolic Problems written by S. 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 2004 with Mathematics categories.

The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection methodand prove theorems of convergence, conditional stability, and other properties of the mentioned methods.

Inverse And Ill Posed Problems

DOWNLOAD
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.

Operator Theory And Ill Posed Problems

DOWNLOAD
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.

Well Posed Ill Posed And Intermediate Problems With Applications

DOWNLOAD
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.

Computational Methods For Applied Inverse Problems

DOWNLOAD
Author : Yanfei Wang
language : en
Publisher: Walter de Gruyter
Release Date : 2012-10-30

Computational Methods For Applied Inverse Problems written by Yanfei Wang 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 2012-10-30 with Mathematics categories.

Nowadays inverse problems and applications in science and engineering represent an extremely active research field. The subjects are related to mathematics, physics, geophysics, geochemistry, oceanography, geography and remote sensing, astronomy, biomedicine, and other areas of applications. This monograph reports recent advances of inversion theory and recent developments with practical applications in frontiers of sciences, especially inverse design and novel computational methods for inverse problems. The practical applications include inverse scattering, chemistry, molecular spectra data processing, quantitative remote sensing inversion, seismic imaging, oceanography, and astronomical imaging. The book serves as a reference book and readers who do research in applied mathematics, engineering, geophysics, biomedicine, image processing, remote sensing, and environmental science will benefit from the contents since the book incorporates a background of using statistical and non-statistical methods, e.g., regularization and optimization techniques for solving practical inverse problems.

Inverse Problems And Carleman Estimates

DOWNLOAD
Author : Michael V. Klibanov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-09-07

Inverse Problems And Carleman Estimates written by Michael V. Klibanov 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 2021-09-07 with Mathematics categories.

This book summarizes the main analytical and numerical results of Carleman estimates. In the analytical part, Carleman estimates for three main types of Partial Differential Equations (PDEs) are derived. In the numerical part, first numerical methods are proposed to solve ill-posed Cauchy problems for both linear and quasilinear PDEs. Next, various versions of the convexification method are developed for a number of Coefficient Inverse Problems.

Gas Dynamics With Applications In Industry And Life Sciences

DOWNLOAD
Author : Mohammad Asadzadeh
language : en
Publisher: Springer Nature
Release Date : 2023-10-30

Gas Dynamics With Applications In Industry And Life Sciences written by Mohammad Asadzadeh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-30 with Mathematics categories.

This proceedings volume gathers selected contributions presented at two instances of the "JSPS/SAC Seminar: On Gas Kinetic/Dynamics and Life Science", held by the Chalmers University of Technology and University of Gothenburg, Sweden, on March 25-26, 2021 (virtual) and March 17-18, 2022 (virtual). Works in this book provide a concise approach to the theoretical and numerical analysis of kinetic type equations that arise, for example, in modeling industrial, medical, and environmental problems. Readers will find some of the most recent theoretical results, newly developed numerical methods in the field, and some open problems. Possible application areas encompass fission/fusion energy, electromagnetics, nuclear science and engineering, medical service, radiation oncology, and plants growth conditions, to name a few. The JSPS/SAC seminars are jointly organized by JSPS (Japan Society for the Promotion of Science)—Stockholm Office and the Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg, Sweden. These seminars foster discussions on the mathematical theory, industrial and life science applications, and numerical analysis of non-linear hyperbolic partial differential equations modeling collision-less plasma and charged particles. Chapter 4 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com. Chapter 11 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Nonlinear And Inverse Problems In Electromagnetics

DOWNLOAD
Author : L. Beilina
language : en
Publisher: Springer
Release Date : 2018-07-19

Nonlinear And Inverse Problems In Electromagnetics written by L. Beilina and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-19 with Mathematics categories.

This volume provides academic discussion on the theory and practice of mathematical analysis of nonlinear and inverse problems in electromagnetics and their applications. From mathematical problem statement to numerical results, the featured articles provide a concise overview of comprehensive approaches to the solution of problems. Articles highlight the most recent research concerning reliable theoretical approaches and numerical techniques and cover a wide range of applications, including acoustics, electromagnetics, optics, medical imaging, and geophysics. The nonlinear and ill-posed nature of inverse problems and the challenges they present when developing new numerical methods are explained, and numerical verification of proposed new methods on simulated and experimental data is provided. Based on the special session of the same name at the 2017 Progress in Electromagnetics Research Symposium, this book offers a platform for interaction between theoretical and practical researchers and between senior and incoming members in the field.

Investigation Methods For Inverse Problems

DOWNLOAD
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.