Multidimensional Inverse and Ill-Posed Problems for Differential Equations:

Multidimensional Inverse and Ill-Posed Problems for Differential Equations:

Author: I︠U︡riĭ Evgenʹevich Anikonov

Publisher: VSP

Published: 1995

Total Pages: 148

ISBN-13: 9789067641852

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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.


Book Synopsis Multidimensional Inverse and Ill-Posed Problems for Differential Equations: by : I︠U︡riĭ Evgenʹevich Anikonov

Download or read book Multidimensional Inverse and Ill-Posed Problems for Differential Equations: written by I︠U︡riĭ Evgenʹevich Anikonov and published by VSP. This book was released on 1995 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Multidimensional Inverse and Ill-Posed Problems for Differential Equations

Author: Yu. E. Anikonov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-07-24

Total Pages: 140

ISBN-13: 3110271478

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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.


Book Synopsis Multidimensional Inverse and Ill-Posed Problems for Differential Equations by : Yu. E. Anikonov

Download or read book Multidimensional Inverse and Ill-Posed Problems for Differential Equations written by Yu. E. Anikonov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Multidimensional Inverse and Ill-posed Problems for Differential Equations

Author: Jurij Evgenʹevič Anikonov

Publisher:

Published: 1995

Total Pages:

ISBN-13:

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Book Synopsis Multidimensional Inverse and Ill-posed Problems for Differential Equations by : Jurij Evgenʹevič Anikonov

Download or read book Multidimensional Inverse and Ill-posed Problems for Differential Equations written by Jurij Evgenʹevič Anikonov and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ill-posed Problems of Mathematical Physics and Analysis

Ill-posed Problems of Mathematical Physics and Analysis

Author: Mikhail Mikha_lovich Lavrent_ev

Publisher: American Mathematical Soc.

Published: 1986-12-31

Total Pages: 300

ISBN-13: 9780821898147

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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


Book Synopsis Ill-posed Problems of Mathematical Physics and Analysis by : Mikhail Mikha_lovich Lavrent_ev

Download or read book Ill-posed Problems of Mathematical Physics and Analysis written by Mikhail Mikha_lovich Lavrent_ev and published by American Mathematical Soc.. This book was released on 1986-12-31 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Inverse Problems in Partial Differential Equations

Author: David L. Colton

Publisher: SIAM

Published: 1990-01-01

Total Pages: 234

ISBN-13: 9780898712520

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Book Synopsis Inverse Problems in Partial Differential Equations by : David L. Colton

Download or read book Inverse Problems in Partial Differential Equations written by David L. Colton and published by SIAM. This book was released on 1990-01-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Small Parameter Method in Multidimensional Inverse Problems

Small Parameter Method in Multidimensional Inverse Problems

Author: A. S. Barashkov

Publisher: VSP

Published: 1998-01-01

Total Pages: 148

ISBN-13: 9789067642958

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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.


Book Synopsis Small Parameter Method in Multidimensional Inverse Problems by : A. S. Barashkov

Download or read book Small Parameter Method in Multidimensional Inverse Problems written by A. S. Barashkov and published by VSP. This book was released on 1998-01-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Inverse Problems

Author: Alexander G. Ramm

Publisher: Springer Science & Business Media

Published: 2005-12-19

Total Pages: 453

ISBN-13: 0387232184

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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.


Book Synopsis Inverse Problems by : Alexander G. Ramm

Download or read book Inverse Problems written by Alexander G. Ramm and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Well-posed, Ill-posed, and Intermediate Problems with Applications

Author: Petrov Yuri P.

Publisher: Walter de Gruyter

Published: 2011-12-22

Total Pages: 245

ISBN-13: 3110195305

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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.


Book Synopsis Well-posed, Ill-posed, and Intermediate Problems with Applications by : Petrov Yuri P.

Download or read book Well-posed, Ill-posed, and Intermediate Problems with Applications written by Petrov Yuri P. and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multidimensional Inverse Problems for Differential Equations

Multidimensional Inverse Problems for Differential Equations

Author: M. M. Lavrentiev

Publisher: Springer

Published: 2006-11-15

Total Pages: 65

ISBN-13: 3540364048

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Book Synopsis Multidimensional Inverse Problems for Differential Equations by : M. M. Lavrentiev

Download or read book Multidimensional Inverse Problems for Differential Equations written by M. M. Lavrentiev and published by Springer. This book was released on 2006-11-15 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multidimensional Inverse and Ill-posed for Differential Equations

Multidimensional Inverse and Ill-posed for Differential Equations

Author: Yu. E. Anikonov

Publisher:

Published: 1995

Total Pages: 133

ISBN-13:

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Book Synopsis Multidimensional Inverse and Ill-posed for Differential Equations by : Yu. E. Anikonov

Download or read book Multidimensional Inverse and Ill-posed for Differential Equations written by Yu. E. Anikonov and published by . This book was released on 1995 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: