Multidimensional Inverse And Ill Posed Problems For Differential Equations

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Multidimensional Inverse And Ill Posed Problems For Differential Equations

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Author : Yu. E. Anikonov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-07-24

Multidimensional Inverse And Ill Posed Problems For Differential Equations written by Yu. E. Anikonov 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.

Inverse problems are usually nonlinear and are separated into one-dimensional and multidimensional problems, depending on whether the sought function (or functions) is a function of one variable or of many. Multidimensionality of inverse problems has particular value at present, because practice shows that many investigating processes are described by an equation, of which the co-efficient essentially depends on many variables. This monograph is devoted to statements of multidimensional inverse problems, in particular to methods of their investigation. Questions of the uniqueness of solution, solvability and stability are studied. Methods to construct a solution are given and, in certain cases, inversion formulas are given as well. Concrete applications of the theory developed here are also given. Where possible, the author has stopped to consider the method of investigation of the problems, thereby sometimes losing generality and quantity of the problems, which can be examined by such a method. The book should be of interet to researchers in the field of applied mathematics, geophysics and mathematical biology.

Multidimensional Inverse And Ill Posed Problems For Differential Equations

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Author : I︠U︡riĭ Evgenʹevich Anikonov
language : en
Publisher: VSP
Release Date : 1995

Multidimensional Inverse And Ill Posed Problems For Differential Equations written by I︠U︡riĭ Evgenʹevich Anikonov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Architecture categories.

This monograph is devoted to statements of multidimensional inverse problems, in particular to methods of their investigation. Questions of the uniqueness of solution, solvability and stability are studied. Methods to construct a solution are given and, in certain cases, inversion formulas are given as well. Concrete applications of the theory developed here are also given. Where possible, the author has stopped to consider the method of investigation of the problems, thereby sometimes losing generality and quantity of the problems, which can be examined by such a method. The book should be of interet to researchers in the field of applied mathematics, geophysics and mathematical biology.

Multidimensional Inverse And Ill Posed Problems For Differential Equations

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Author : Jurij Evgenʹevič Anikonov
language : en
Publisher:
Release Date : 1995

Multidimensional Inverse And Ill Posed Problems For Differential Equations written by Jurij Evgenʹevič Anikonov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.

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

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.

Small Parameter Method In Multidimensional Inverse Problems

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Author : A. S. Barashkov
language : en
Publisher: VSP
Release Date : 1998-01-01

Small Parameter Method In Multidimensional Inverse Problems written by A. S. Barashkov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.

Inverse problem theory is one of the most important directions of modern mathematics. In this monograph, for the most part, inverse coefficient problems are explored, for example Helmholtz equations. The coefficient of these equations need to be recovered by certain known information on the solutions of these equations. In this book, the basic method for studying multidimensional inverse problems is the small parameter method (the asymptotic method). Such methods are widely used for investigation of direct problems.

Inverse Problems

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Author : Alexander G. Ramm
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-19

Inverse Problems written by Alexander G. Ramm and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-19 with Technology & Engineering 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.

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.

Inverse Problems For Kinetic And Other Evolution Equations

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Author : I︠U︡riĭ Evgenʹevich Anikonov
language : en
Publisher: VSP
Release Date : 2001

Inverse Problems For Kinetic And Other Evolution Equations written by I︠U︡riĭ Evgenʹevich Anikonov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

This monograph in the "Inverse and Ill-Posed Problems Series deals with methods of studying multidimensional inverse problems for kinetic and other evolution equations, in particular transfer equations. The methods used are applied to concrete inverse problems, especially multidimensional inverse problems applicable in linear and nonlinear statements.A significant part of the book contains formulas and relations for solving inverse problems, including formulas for the solution and coefficients of kinetic equations, differential-difference equations, nonlinear evolution equations, and second order equations.This monograph will be of value and interest to mathematicians, engineers and other specialists dealing with inverse and ill posed problems.

Direct Methods Of Solving Multidimensional Inverse Hyperbolic Problems

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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.