Inverse Problems for Kinetic and Other Evolution Equations PDF Download
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Author: Yu. E. Anikonov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110940906
Category : Mathematics
Languages : en
Pages : 280
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Book Description
This monograph 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.
Author: Yu. E. Anikonov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110940906
Category : Mathematics
Languages : en
Pages : 280
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Book Description
This monograph 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.
Author: I︠U︡riĭ Evgenʹevich Anikonov
Publisher: VSP
ISBN: 9789067643450
Category : Mathematics
Languages : en
Pages : 288
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Book Description
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.
Author: A. S. Blagoveshchenskii
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110940892
Category : Mathematics
Languages : en
Pages : 148
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Book Description
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.
Author: Mikhail M. Lavrent'ev
Publisher: Walter de Gruyter
ISBN: 3110915529
Category : Mathematics
Languages : en
Pages : 288
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Book Description
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.
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: 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: 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: S. P. Shishatskii
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110920328
Category : Mathematics
Languages : en
Pages : 192
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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: Vladimir G. Romanov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110942011
Category : Mathematics
Languages : en
Pages : 484
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Book Description
M.M. Lavrentiev is the author of many fundamental scientific results in many directions of mathematics and its applications, such as differential equations, inverse and ill-posed problems, tomography, numerical and applied mathematics. His results in the theory of inverse problems for differential equations and in tomography are well known all over the world. To honour him on the occasion of his 70th birthday renowned scientists in this field of mathematics, both from East and West, have contributed to this special collection of papers on ill-posed and inverse problems, which will be of interest to anyone working in this field.
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.
