Download or read book Inverse Logarithmic Potential Problem written by V. G. Cherednichenko and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 256 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.

Download or read book Logarithmic Potentials with External Fields written by Edward B. Saff and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems. This is due to the interaction of approximation theoretical techniques with classical potential theory (more precisely, the theory of logarithmic potentials, which is directly related to polynomials and to problems in the plane or on the real line). Most of the applications are based on an exten sion of classical logarithmic potential theory to the case when there is a weight (external field) present. The list of recent developments is quite impressive and includes: creation of the theory of non-classical orthogonal polynomials with re spect to exponential weights; the theory of orthogonal polynomials with respect to general measures with compact support; the theory of incomplete polynomials and their widespread generalizations, and the theory of multipoint Pade approximation. The new approach has produced long sought solutions for many problems; most notably, the Freud problems on the asymptotics of orthogonal polynomials with a respect to weights of the form exp(-Ixl ); the "l/9-th" conjecture on rational approximation of exp(x); and the problem of the exact asymptotic constant in the rational approximation of Ixl. One aim of the present book is to provide a self-contained introduction to the aforementioned "weighted" potential theory as well as to its numerous applications. As a side-product we shall also fully develop the classical theory of logarithmic potentials.

Download or read book The Logarithmic Potential written by Griffith Conrad Evans and published by . This book was released on 1927 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies fundamental properties of the logarithmic potential and their connections to the theory of Fourier series, to potential theory, and to function theory. The material centers around a study of Poisson's integral in two dimensions and of the corresponding Stieltjes integral. The results are then extended to the integrals in terms of Green's functions for general regions. There are some thirty exercises scattered throughout the text. These are designed in part to familiarize the reader with the concepts introduced, and in part to complement the theory. The reader should know something of potential theory, functions of a complex variable, and Lebesgue integrals. The book is based on lectures given by the author in 1924-1925 at the Rice Institute and at the University of Chicago.

Download or read book Methods for Solving Inverse Problems in Mathematical Physics written by Global Express Ltd. Co. and published by CRC Press. This book was released on 2000-03-21 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, app

Download or read book Integral Geometry and Inverse Problems for Hyperbolic Equations written by V. G. Romanov and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are currently many practical situations in which one wishes to determine the coefficients in an ordinary or partial differential equation from known functionals of its solution. These are often called "inverse problems of mathematical physics" and may be contrasted with problems in which an equation is given and one looks for its solution under initial and boundary conditions. Although inverse problems are often ill-posed in the classical sense, their practical importance is such that they may be considered among the pressing problems of current mathematical re search. A. N. Tihonov showed [82], [83] that there is a broad class of inverse problems for which a particular non-classical definition of well-posed ness is appropriate. This new definition requires that a solution be unique in a class of solutions belonging to a given subset M of a function space. The existence of a solution in this set is assumed a priori for some set of data. The classical requirement of continuous dependence of the solution on the data is retained but it is interpreted differently. It is required that solutions depend continuously only on that data which does not take the solutions out of M.

Download or read book Elements of the Theory of Inverse Problems written by A. M. Denisov 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: 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.

Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Inverse Problems in Differential Equations written by G. Anger and published by Springer Science & Business Media. This book was released on 1990-06-30 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elucidates the fundamental mathematical structures of inverse problems, analyzing both the information content and the solution of some inverse problems in which the information content of the coefficients and the source term of a given differential equation is not too large. In order to be accessib

Download or read book Investigation Methods for Inverse Problems written by Vladimir G. Romanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-10 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

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.

Download or read book Method of Spectral Mappings in the Inverse Problem Theory written by Vacheslav A. Yurko and published by Walter de Gruyter. This book was released on 2013-10-10 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.).

Download or read book Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems written by Sergey I. Kabanikhin and published by Walter de Gruyter. This book was released on 2013-04-09 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection method and prove theorems of convergence, conditional stability, and other properties of the mentioned methods.

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.

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.

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.