Inverse Problems Of Wave Processes

Author : A. S. Blagoveshchenskii
Publisher : Walter de Gruyter GmbH & Co KG
Page : 148 pages
File Size : 48,9 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110940893

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Inverse Problems of Wave Processes by A. S. Blagoveshchenskii Pdf

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 : Graham M. L. Gladwell,Antonino Morassi
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 41,9 Mb
Release : 2011-05-25
Category : Technology & Engineering
ISBN : 9783709106969

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Dynamical Inverse Problems: Theory and Application by Graham M. L. Gladwell,Antonino Morassi Pdf

The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.

Author : P. G. Danilaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 128 pages
File Size : 54,5 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110940916

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Coefficient Inverse Problems for Parabolic Type Equations and Their Application by P. G. Danilaev Pdf

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 : Mikhail M. Lavrent'ev,Alexander V. Avdeev,Viatcheslav I. Priimenko
Publisher : Walter de Gruyter
Page : 288 pages
File Size : 40,5 Mb
Release : 2012-05-07
Category : Mathematics
ISBN : 9783110915525

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Inverse Problems of Mathematical Physics by Mikhail M. Lavrent'ev,Alexander V. Avdeev,Viatcheslav I. Priimenko Pdf

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 : Vyacheslav I. Maksimov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 280 pages
File Size : 45,6 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110944839

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Dynamical Inverse Problems of Distributed Systems by Vyacheslav I. Maksimov Pdf

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.).

Author : Vladimir G. Romanov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 292 pages
File Size : 43,9 Mb
Release : 2014-10-10
Category : Mathematics
ISBN : 9783110943849

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Investigation Methods for Inverse Problems by Vladimir G. Romanov Pdf

This monograph deals with some inverse problems of mathematical physics. It introduces new methods for studying inverse problems and gives obtained results, which are related to the conditional well posedness of the problems. The main focus lies on time-domain inverse problems for hyperbolic equations and the kinetic transport equation.

Author : Michael V. Klibanov,Alexander A. Timonov
Publisher : Walter de Gruyter
Page : 292 pages
File Size : 51,9 Mb
Release : 2012-04-17
Category : Mathematics
ISBN : 9783110915549

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Carleman Estimates for Coefficient Inverse Problems and Numerical Applications by Michael V. Klibanov,Alexander A. Timonov Pdf

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 : Yurii Ya. Belov
Publisher : Walter de Gruyter
Page : 220 pages
File Size : 48,9 Mb
Release : 2012-02-14
Category : Mathematics
ISBN : 9783110944631

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Inverse Problems for Partial Differential Equations by Yurii Ya. Belov Pdf

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
Page : 244 pages
File Size : 40,7 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9783110944983

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

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 : Anvar Kh. Amirov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 212 pages
File Size : 48,7 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110940947

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Integral Geometry and Inverse Problems for Kinetic Equations by Anvar Kh. Amirov Pdf

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.

Author : I︠U︡riĭ Evgenʹevich Anikonov,IUri i Evgen'evich Anikonov
Publisher : VSP
Page : 288 pages
File Size : 40,6 Mb
Release : 2001
Category : Mathematics
ISBN : 9067643459

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Inverse Problems for Kinetic and Other Evolution Equations by I︠U︡riĭ Evgenʹevich Anikonov,IUri i Evgen'evich Anikonov Pdf

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 : Yu. E. Anikonov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 280 pages
File Size : 40,5 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110940909

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Inverse Problems for Kinetic and Other Evolution Equations by Yu. E. Anikonov Pdf

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 : Vacheslav A. Yurko
Publisher : Walter de Gruyter
Page : 316 pages
File Size : 42,8 Mb
Release : 2013-10-10
Category : Mathematics
ISBN : 9783110940961

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Method of Spectral Mappings in the Inverse Problem Theory by Vacheslav A. Yurko Pdf

Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science. This monograph is devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory. The book consists of three chapters: In Chapter 1 the method of spectral mappings is presented in the simplest version for the Sturm-Liouville operator. In Chapter 2 the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3 inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.

Author : Khosrow Chadan,Pierre C. Sabatier
Publisher : Springer Science & Business Media
Page : 526 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642833175

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Inverse Problems in Quantum Scattering Theory by Khosrow Chadan,Pierre C. Sabatier Pdf

The normal business of physicists may be schematically thought of as predic ting the motions of particles on the basis of known forces, or the propagation of radiation on the basis of a known constitution of matter. The inverse problem is to conclude what the forces or constitutions are on the basis of the observed motion. A large part of our sensory contact with the world around us depends on an intuitive solution of such an inverse problem: We infer the shape, size, and surface texture of external objects from their scattering and absorption of light as detected by our eyes. When we use scattering experiments to learn the size or shape of particles, or the forces they exert upon each other, the nature of the problem is similar, if more refined. The kinematics, the equations of motion, are usually assumed to be known. It is the forces that are sought, and how they vary from point to point. As with so many other physical ideas, the first one we know of to have touched upon the kind of inverse problem discussed in this book was Lord Rayleigh (1877). In the course of describing the vibrations of strings of variable density he briefly discusses the possibility of inferring the density distribution from the frequencies of vibration. This passage may be regarded as a precursor of the mathematical study of the inverse spectral problem some seventy years later.

Author : K. Chadan,P. C. Sabatier
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 53,6 Mb
Release : 2013-04-18
Category : Science
ISBN : 9783662121252

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Inverse Problems in Quantum Scattering Theory by K. Chadan,P. C. Sabatier Pdf