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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 of Mathematical Physics

Author: Mikhail M. Lavrent'ev

Publisher: Walter de Gruyter

Published: 2012-05-07

Total Pages: 288

ISBN-13: 3110915529

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This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.

Book Synopsis Inverse Problems of Mathematical Physics by : Mikhail M. Lavrent'ev

Download or read book Inverse Problems of Mathematical Physics written by Mikhail M. Lavrent'ev and published by Walter de Gruyter. This book was released on 2012-05-07 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.

Dynamical Inverse Problems of Distributed Systems

Author: Vyacheslav I. Maksimov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-07-24

Total Pages: 280

ISBN-13: 3110944839

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This monograph deals with problems of dynamical reconstruction of unknown variable characteristics (distributed or boundary disturbances, coefficients of operator etc.) for various classes of systems with distributed parameters (parabolic and hyperbolic equations, evolutionary variational inequalities etc.).

Book Synopsis Dynamical Inverse Problems of Distributed Systems by : Vyacheslav I. Maksimov

Download or read book Dynamical Inverse Problems of Distributed Systems written by Vyacheslav I. Maksimov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with problems of dynamical reconstruction of unknown variable characteristics (distributed or boundary disturbances, coefficients of operator etc.) for various classes of systems with distributed parameters (parabolic and hyperbolic equations, evolutionary variational inequalities etc.).

Carleman Estimates for Coefficient Inverse Problems and Numerical Applications

Author: Michael V. Klibanov

Publisher: Walter de Gruyter

Published: 2012-04-17

Total Pages: 292

ISBN-13: 3110915545

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In this monograph, the main subject of the author's considerations is coefficient inverse problems. Arising in many areas of natural sciences and technology, such problems consist of determining the variable coefficients of a certain differential operator defined in a domain from boundary measurements of a solution or its functionals. Although the authors pay strong attention to the rigorous justification of known results, they place the primary emphasis on new concepts and developments.

Book Synopsis Carleman Estimates for Coefficient Inverse Problems and Numerical Applications by : Michael V. Klibanov

Download or read book Carleman Estimates for Coefficient Inverse Problems and Numerical Applications written by Michael V. Klibanov and published by Walter de Gruyter. This book was released on 2012-04-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the main subject of the author's considerations is coefficient inverse problems. Arising in many areas of natural sciences and technology, such problems consist of determining the variable coefficients of a certain differential operator defined in a domain from boundary measurements of a solution or its functionals. Although the authors pay strong attention to the rigorous justification of known results, they place the primary emphasis on new concepts and developments.

Forward and Inverse Problems for Hyperbolic, Elliptic and Mixed Type Equations

Author: Alexander G. Megrabov

Publisher: Walter de Gruyter

Published: 2012-05-24

Total Pages: 244

ISBN-13: 3110944987

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Inverse problems are an important and rapidly developing direction in mathematics, mathematical physics, differential equations, and various applied technologies (geophysics, optic, tomography, remote sensing, radar-location, etc.). In this monograph direct and inverse problems for partial differential equations are considered. The type of equations focused are hyperbolic, elliptic, and mixed (elliptic-hyperbolic). The direct problems arise as generalizations of problems of scattering plane elastic or acoustic waves from inhomogeneous layer (or from half-space). The inverse problems are those of determination of medium parameters by giving the forms of incident and reflected waves or the vibrations of certain points of the medium. The method of research of all inverse problems is spectral-analytical, consisting in reducing the considered inverse problems to the known inverse problems for the Sturm-Liouville equation or the string equation. Besides the book considers discrete inverse problems. In these problems an arbitrary set of point sources (emissive sources, oscillators, point masses) is determined.

Book Synopsis Forward and Inverse Problems for Hyperbolic, Elliptic and Mixed Type Equations by : Alexander G. Megrabov

Download or read book Forward and Inverse Problems for Hyperbolic, Elliptic and Mixed Type Equations written by Alexander G. Megrabov and published by Walter de Gruyter. This book was released on 2012-05-24 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are an important and rapidly developing direction in mathematics, mathematical physics, differential equations, and various applied technologies (geophysics, optic, tomography, remote sensing, radar-location, etc.). In this monograph direct and inverse problems for partial differential equations are considered. The type of equations focused are hyperbolic, elliptic, and mixed (elliptic-hyperbolic). The direct problems arise as generalizations of problems of scattering plane elastic or acoustic waves from inhomogeneous layer (or from half-space). The inverse problems are those of determination of medium parameters by giving the forms of incident and reflected waves or the vibrations of certain points of the medium. The method of research of all inverse problems is spectral-analytical, consisting in reducing the considered inverse problems to the known inverse problems for the Sturm-Liouville equation or the string equation. Besides the book considers discrete inverse problems. In these problems an arbitrary set of point sources (emissive sources, oscillators, point masses) is determined.

Inverse Problems for Partial Differential Equations

Author: Yurii Ya. Belov

Publisher: Walter de Gruyter

Published: 2012-02-14

Total Pages: 220

ISBN-13: 3110944634

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This monograph is devoted to identification problems of coefficients in equations of mathematical physics. It invesitgates the existence and uniqueness of the solutions for identification coefficient problems in parabolic and hyperbolic equations and equation systems of composite type. The problems are studied with the Cauchy data and equations in which the Fourier transform with respect to the chosen variable is supposed to occur. Differential properties of the solutions for the original direct problems and their behavior under great values of time are studied on the basis of solution properties for direct problems. The identification problems with one or two unknown coefficients are also investigated. For initial boundary value conditions linear and nonlinear parabolic equations are studied.

Book Synopsis Inverse Problems for Partial Differential Equations by : Yurii Ya. Belov

Download or read book Inverse Problems for Partial Differential Equations written by Yurii Ya. Belov and published by Walter de Gruyter. This book was released on 2012-02-14 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to identification problems of coefficients in equations of mathematical physics. It invesitgates the existence and uniqueness of the solutions for identification coefficient problems in parabolic and hyperbolic equations and equation systems of composite type. The problems are studied with the Cauchy data and equations in which the Fourier transform with respect to the chosen variable is supposed to occur. Differential properties of the solutions for the original direct problems and their behavior under great values of time are studied on the basis of solution properties for direct problems. The identification problems with one or two unknown coefficients are also investigated. For initial boundary value conditions linear and nonlinear parabolic equations are studied.

Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography-Type Projection Data

Author: V. P. Golubyatnikov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-07-24

Total Pages: 132

ISBN-13: 311092031X

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The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Book Synopsis Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography-Type Projection Data by : V. P. Golubyatnikov

Download or read book Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography-Type Projection Data written by V. P. Golubyatnikov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Coefficient Inverse Problems for Parabolic Type Equations and Their Application

Author: P. G. Danilaev

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-07-24

Total Pages: 128

ISBN-13: 3110940914

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As a rule, many practical problems are studied in a situation when the input data are incomplete. For example, this is the case for a parabolic partial differential equation describing the non-stationary physical process of heat and mass transfer if it contains the unknown thermal conductivity coefficient. Such situations arising in physical problems motivated the appearance of the present work. In this monograph the author considers numerical solutions of the quasi-inversion problems, to which the solution of the original coefficient inverse problems are reduced. Underground fluid dynamics is taken as a field of practical use of coefficient inverse problems. The significance of these problems for this application domain consists in the possibility to determine the physical fields of parameters that characterize the filtration properties of porous media (oil strata). This provides the possibility of predicting the conditions of oil-field development and the effects of the exploitation. The research carried out by the author showed that the quasi-inversion method can be applied also for solution of "interior coefficient inverse problems" by reducing them to the problem of continuation of a solution to a parabolic equation. This reduction is based on the results of the proofs of the uniqueness theorems for solutions of the corresponding coefficient inverse problems.

Book Synopsis Coefficient Inverse Problems for Parabolic Type Equations and Their Application by : P. G. Danilaev

Download or read book Coefficient Inverse Problems for Parabolic Type Equations and Their Application written by P. G. Danilaev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a rule, many practical problems are studied in a situation when the input data are incomplete. For example, this is the case for a parabolic partial differential equation describing the non-stationary physical process of heat and mass transfer if it contains the unknown thermal conductivity coefficient. Such situations arising in physical problems motivated the appearance of the present work. In this monograph the author considers numerical solutions of the quasi-inversion problems, to which the solution of the original coefficient inverse problems are reduced. Underground fluid dynamics is taken as a field of practical use of coefficient inverse problems. The significance of these problems for this application domain consists in the possibility to determine the physical fields of parameters that characterize the filtration properties of porous media (oil strata). This provides the possibility of predicting the conditions of oil-field development and the effects of the exploitation. The research carried out by the author showed that the quasi-inversion method can be applied also for solution of "interior coefficient inverse problems" by reducing them to the problem of continuation of a solution to a parabolic equation. This reduction is based on the results of the proofs of the uniqueness theorems for solutions of the corresponding coefficient inverse problems.

Inverse Problems of Wave Processes

Author: A. S. Blagoveshchenskii

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-07-24

Total Pages: 148

ISBN-13: 3110940892

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This monograph covers dynamical inverse problems, that is problems whose data are the values of wave fields. It deals with the problem of determination of one or more coefficients of a hyperbolic equation or a system of hyperbolic equations. The desired coefficients are functions of point. Most attention is given to the case where the required functions depend only on one coordinate. The first chapter of the book deals mainly with methods of solution of one-dimensional inverse problems. The second chapter focuses on scalar inverse problems of wave propagation in a layered medium. In the final chapter inverse problems for elasticity equations in stratified media and acoustic equations for moving media are given.

Book Synopsis Inverse Problems of Wave Processes by : A. S. Blagoveshchenskii

Download or read book Inverse Problems of Wave Processes written by A. S. Blagoveshchenskii and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers dynamical inverse problems, that is problems whose data are the values of wave fields. It deals with the problem of determination of one or more coefficients of a hyperbolic equation or a system of hyperbolic equations. The desired coefficients are functions of point. Most attention is given to the case where the required functions depend only on one coordinate. The first chapter of the book deals mainly with methods of solution of one-dimensional inverse problems. The second chapter focuses on scalar inverse problems of wave propagation in a layered medium. In the final chapter inverse problems for elasticity equations in stratified media and acoustic equations for moving media are given.

Integral Geometry and Inverse Problems for Kinetic Equations

Author: Anvar Kh. Amirov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-07-24

Total Pages: 212

ISBN-13: 3110940949

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In this monograph a method for proving the solvability of integral geometry problems and inverse problems for kinetic equations is presented. The application of this method has led to interesting problems of the Dirichlet type for third order differential equations, the solvability of which appears to depend on the geometry of the domain for which the problem is stated. Another considered subject is the problem of integral geometry on paraboloids, in particular the uniqueness of solutions to the Goursat problem for a differential inequality, which implies new theorems on the uniqueness of solutions to this problem for a class of quasilinear hyperbolic equations. A class of multidimensional inverse problems associated with problems of integral geometry and the inverse problem for the quantum kinetic equations are also included.

Book Synopsis Integral Geometry and Inverse Problems for Kinetic Equations by : Anvar Kh. Amirov

Download or read book Integral Geometry and Inverse Problems for Kinetic Equations written by Anvar Kh. Amirov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph a method for proving the solvability of integral geometry problems and inverse problems for kinetic equations is presented. The application of this method has led to interesting problems of the Dirichlet type for third order differential equations, the solvability of which appears to depend on the geometry of the domain for which the problem is stated. Another considered subject is the problem of integral geometry on paraboloids, in particular the uniqueness of solutions to the Goursat problem for a differential inequality, which implies new theorems on the uniqueness of solutions to this problem for a class of quasilinear hyperbolic equations. A class of multidimensional inverse problems associated with problems of integral geometry and the inverse problem for the quantum kinetic equations are also included.