Download or read book Volterra Equations and Inverse Problems written by A. L. Bughgeim 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: 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 Nonclassical Linear Volterra Equations of the First Kind written by Anatoly S. Apartsyn and published by Walter de Gruyter. This book was released on 2011-03-01 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with linear integra Volterra equations of the first kind with variable upper and lower limits of integration. Volterra operators of this type are the basic operators for integral models of dynamic systems.

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 Coefficient Inverse Problems for Parabolic Type Equations and Their Application written by P. G. Danilaev and published by VSP. This book was released on 2001-01-01 with total page 136 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 monographthe 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 Inverse Problems for Maxwell s Equations written by V. G. Romanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-10 with total page 260 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 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 Surveys on Solution Methods for Inverse Problems written by David Colton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are concerned with determining causes for observed or desired effects. Problems of this type appear in many application fields both in science and in engineering. The mathematical modelling of inverse problems usually leads to ill-posed problems, i.e., problems where solutions need not exist, need not be unique or may depend discontinuously on the data. For this reason, numerical methods for solving inverse problems are especially difficult, special methods have to be developed which are known under the term "regularization methods". This volume contains twelve survey papers about solution methods for inverse and ill-posed problems and about their application to specific types of inverse problems, e.g., in scattering theory, in tomography and medical applications, in geophysics and in image processing. The papers have been written by leading experts in the field and provide an up-to-date account of solution methods for inverse problems.

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 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 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 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 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.

Download or read book Linear Sobolev Type Equations and Degenerate Semigroups of Operators written by Georgy A. Sviridyuk and published by Walter de Gruyter. This book was released on 2012-06-04 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the mathematics, and providing only a minimum of explicatory comment, this volume contains six chapters covering auxiliary material, relatively p-radial operators, relatively p-sectorial operators, relatively σ-bounded operators, Cauchy problems for inhomogenous Sobolev-type equations, bounded solutions to Sobolev-type equations, and optimal control.

Download or read book Inverse Problems of Electromagnetic Geophysical Fields written by P. S. Martyshko 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: 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 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.

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