Coefficient Inverse Problems for Parabolic Type Equations and Their Application PDF Download
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Author: P. G. Danilaev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110940914
Category : Mathematics
Languages : en
Pages : 128
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Book Description
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.
Author: P. G. Danilaev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110940914
Category : Mathematics
Languages : en
Pages : 128
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Book Description
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.
Author: Yurii Ya. Belov
Publisher: Walter de Gruyter
ISBN: 3110944634
Category : Mathematics
Languages : en
Pages : 220
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Book Description
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.
Author: Yu. Ya Belov
Publisher: V.S.P. International Science
ISBN: 9789067643580
Category : Mathematics
Languages : en
Pages : 211
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Book Description
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.
Author: David L. Colton
Publisher: SIAM
ISBN: 9780898712520
Category : Mathematics
Languages : en
Pages : 234
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Book Description
Author: Michael V. Klibanov
Publisher: Walter de Gruyter
ISBN: 3110915545
Category : Mathematics
Languages : en
Pages : 292
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Book Description
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.
Author: Wang Quan-Fang
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659709203
Category :
Languages : en
Pages : 184
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Book Description
Two identification issues in inverse problems discussed in this monograph.One is identifying parameters for a class abstract parabolic partial differential equations on Lipschitz continuity.In variational method framework at (complex) Hilbert spaces, applying theoretic results to Hopfield neural network;Cahn-Hilliard equation;Klein-Gordon-Schrodinger equation.Another is time independent coefficient inverse, using Taylor expansion to construct approximate polynomial for convexificaiton approach in global convergent algorithm for 2D parabolic problems.In recovery, determining and reconstructing of system profile, property or characterization, this book captured general issues to identify unknown factors.Proposed abstract theory, bi-quadratic polynomial methodology can be developed to elliptic/hyperbolic issue, or extended to 3D.Rest work focus on time-spatial wise coefficients inverse.To be practical applied to a broad diverse problems in a variety disciplinary.These kinds of behaviors to do certification (e.g.DNA) just like detector to find mystery from witness or doctor to seek sick from symptoms, delighted and stimulated.A great interest would be made sure in the future inverse pr
Author: Petrov Yuri P.
Publisher: Walter de Gruyter
ISBN: 3110195305
Category : Mathematics
Languages : en
Pages : 245
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Book Description
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.
Author: Alexander G. Megrabov
Publisher: Walter de Gruyter
ISBN: 3110944987
Category : Mathematics
Languages : en
Pages : 244
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Book Description
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.
Author: A. Asanov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110900149
Category : Mathematics
Languages : en
Pages : 156
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Book Description
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.
Author: Valentin K. Ivanov
Publisher: Walter de Gruyter
ISBN: 3110944820
Category : Mathematics
Languages : en
Pages : 296
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Book Description
This monograph is a revised and extended version of the Russian edition from 1978. It includes the general theory of linear ill-posed problems concerning e. g. the structure of sets of uniform regularization, the theory of error estimation, and the optimality method. As a distinguishing feature the book considers ill-posed problems not only in Hilbert but also in Banach spaces. It is natural that since the appearance of the first edition considerable progress has been made in the theory of inverse and ill-posed problems as wall as in ist applications. To reflect these accomplishments the authors included additional material e. g. comments to each chapter and a list of monographs with annotations.
