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Small Parameter Method In Multidimensional Inverse Problems
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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.
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.).
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.
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.
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.
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.
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.
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.
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.
Book Synopsis Inverse Problems for Kinetic and Other Evolution Equations by : I︠U︡riĭ Evgenʹevich Anikonov
Download or read book Inverse Problems for Kinetic and Other Evolution Equations written by I︠U︡riĭ Evgenʹevich Anikonov and published by VSP. This book was released on 2001 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Inverse Problems for Kinetic and Other Evolution Equations by : Yu. E. Anikonov
Download or read book Inverse Problems for Kinetic and Other Evolution 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 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Operator Theory and Ill-Posed Problems by : Mikhail M. Lavrent'ev
Download or read book Operator Theory and Ill-Posed Problems written by Mikhail M. Lavrent'ev and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of three major parts. The first two parts deal with general mathematical concepts and certain areas of operator theory. The third part is devoted to ill-posed problems. It can be read independently of the first two parts and presents a good example of applying the methods of calculus and functional analysis. The first part "Basic Concepts" briefly introduces the language of set theory and concepts of abstract, linear and multilinear algebra. Also introduced are the language of topology and fundamental concepts of calculus: the limit, the differential, and the integral. A special section is devoted to analysis on manifolds. The second part "Operators" describes the most important function spaces and operator classes for both linear and nonlinear operators. Different kinds of generalized functions and their transformations are considered. Elements of the theory of linear operators are presented. Spectral theory is given a special focus. The third part "Ill-Posed Problems" is devoted to problems of mathematical physics, integral and operator equations, evolution equations and problems of integral geometry. It also deals with problems of analytic continuation. Detailed coverage of the subjects and numerous examples and exercises make it possible to use the book as a textbook on some areas of calculus and functional analysis. It can also be used as a reference textbook because of the extensive scope and detailed references with comments.
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.
Book Synopsis Ill-Posed Boundary-Value Problems by : Serikkali E. Temirbolat
Download or read book Ill-Posed Boundary-Value Problems written by Serikkali E. Temirbolat and published by Walter de Gruyter. This book was released on 2012-06-04 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph extends well-known facts to new classes of problems and works out novel approaches to the solution of these problems. It is devoted to the questions of ill-posed boundary-value problems for systems of various types of the first-order differential equations with constant coefficients and the methods for their solution.
Book Synopsis Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis by : Mikhail M. Lavrent'ev
Download or read book Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis written by Mikhail M. Lavrent'ev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings of the international Conference "Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis", held at the Samarkand State University, Uzbekistan in September 2000 bring together fundamental research articles in the major areas of the numerated fields of analysis and mathematical physics. The book covers the following topics: theory of ill-posed problems inverse problems for differential equations boundary value problems for equations of mixed type integral geometry mathematical modelling and numerical methods in natural sciences
Book Synopsis Theory of Linear Ill-Posed Problems and its Applications by : Valentin K. Ivanov
Download or read book Theory of Linear Ill-Posed Problems and its Applications written by Valentin K. Ivanov and published by Walter de Gruyter. This book was released on 2013-02-18 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
