Inverse Problems For Kinetic And Other Evolution Equations

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Inverse Problems for Kinetic and Other Evolution Equations

Yu. E. Anikonov
Inverse Problems for Kinetic and Other Evolution Equations Book PDF

Author : Yu. E. Anikonov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 280 pages
File Size : 45,5 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.

Inverse Problems for Kinetic and Other Evolution Equations

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

Author : I︠U︡riĭ Evgenʹevich Anikonov,IUri i Evgen'evich Anikonov
Publisher : VSP
Page : 288 pages
File Size : 43,8 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.

Integral Geometry and Inverse Problems for Kinetic Equations

Anvar Kh. Amirov
Integral Geometry and Inverse Problems for Kinetic Equations Book PDF

Author : Anvar Kh. Amirov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 212 pages
File Size : 48,8 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.

Inverse Problems for Partial Differential Equations

Yurii Ya. Belov
Inverse Problems for Partial Differential Equations Book PDF

Author : Yurii Ya. Belov
Publisher : Walter de Gruyter
Page : 220 pages
File Size : 53,7 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.

Forward and Inverse Problems for Hyperbolic, Elliptic and Mixed Type Equations

Alexander G. Megrabov
Forward and Inverse Problems for Hyperbolic Elliptic and Mixed Type Equations Book PDF

Author : Alexander G. Megrabov
Publisher : Walter de Gruyter
Page : 244 pages
File Size : 43,8 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.

Inverse Problems of Mathematical Physics

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

Author : Mikhail M. Lavrent'ev,Alexander V. Avdeev,Viatcheslav I. Priimenko
Publisher : Walter de Gruyter
Page : 288 pages
File Size : 45,7 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.

Coefficient Inverse Problems for Parabolic Type Equations and Their Application

P. G. Danilaev
Coefficient Inverse Problems for Parabolic Type Equations and Their Application Book PDF

Author : P. G. Danilaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 128 pages
File Size : 45,8 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.

Carleman Estimates for Coefficient Inverse Problems and Numerical Applications

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

Author : Michael V. Klibanov,Alexander A. Timonov
Publisher : Walter de Gruyter
Page : 292 pages
File Size : 53,6 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.

Dynamical Inverse Problems of Distributed Systems

Vyacheslav I. Maksimov
Dynamical Inverse Problems of Distributed Systems Book PDF

Author : Vyacheslav I. Maksimov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 280 pages
File Size : 44,9 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.).

Investigation Methods for Inverse Problems

Vladimir G. Romanov
Investigation Methods for Inverse Problems Book PDF

Author : Vladimir G. Romanov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 292 pages
File Size : 50,5 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.

Method of Spectral Mappings in the Inverse Problem Theory

Vacheslav A. Yurko
Method of Spectral Mappings in the Inverse Problem Theory Book PDF

Author : Vacheslav A. Yurko
Publisher : Walter de Gruyter
Page : 316 pages
File Size : 53,9 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.

Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems

Sergey I. Kabanikhin,Abdigany D. Satybaev,Maxim A. Shishlenin
Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems Book PDF

Author : Sergey I. Kabanikhin,Abdigany D. Satybaev,Maxim A. Shishlenin
Publisher : Walter de Gruyter
Page : 188 pages
File Size : 47,5 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9783110960716

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Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems by Sergey I. Kabanikhin,Abdigany D. Satybaev,Maxim A. Shishlenin Pdf

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.

Ill-Posed Internal Boundary Value Problems for the Biharmonic Equation

Mukarram A. Atakhodzhaev
Ill Posed Internal Boundary Value Problems for the Biharmonic Equation Book PDF

Author : Mukarram A. Atakhodzhaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 168 pages
File Size : 42,5 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110944815

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Ill-Posed Internal Boundary Value Problems for the Biharmonic Equation by Mukarram A. Atakhodzhaev Pdf

Internal boundary value problems deals with the problem of determining the solution of an equation if data are given on two manifolds. One manifold is the domain boundary and the other manifold is situated inside the domain. This monograph studies three essentially ill-posed internal boundary value problems for the biharmonic equation and the Cauchy problem for the abstract biharmonic equation, both qualitatively and quantitatively. In addition, some variants of these problems and the Cauchy problem, as well as the m-dimensional case, are considered. The author introduces some new notions, such as the notion of complete solvability.

Linear Sobolev Type Equations and Degenerate Semigroups of Operators

Georgy A. Sviridyuk,Vladimir E. Fedorov
Linear Sobolev Type Equations and Degenerate Semigroups of Operators Book PDF

Author : Georgy A. Sviridyuk,Vladimir E. Fedorov
Publisher : Walter de Gruyter
Page : 224 pages
File Size : 45,6 Mb
Release : 2012-06-04
Category : Mathematics
ISBN : 9783110915501

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Linear Sobolev Type Equations and Degenerate Semigroups of Operators by Georgy A. Sviridyuk,Vladimir E. Fedorov Pdf

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.

Well-posed, Ill-posed, and Intermediate Problems with Applications

Petrov Yuri P.,Valery S. Sizikov
Well posed Ill posed and Intermediate Problems with Applications Book PDF

Author : Petrov Yuri P.,Valery S. Sizikov
Publisher : Walter de Gruyter
Page : 245 pages
File Size : 45,5 Mb
Release : 2011-12-22
Category : Mathematics
ISBN : 9783110195309

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Well-posed, Ill-posed, and Intermediate Problems with Applications by Petrov Yuri P.,Valery S. Sizikov Pdf

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.