Integral Geometry and Inverse Problems for Kinetic Equations PDF Download
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Author: Anvar Kh. Amirov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110940949
Category : Mathematics
Languages : en
Pages : 212
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Book Description
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: Anvar Kh. Amirov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110940949
Category : Mathematics
Languages : en
Pages : 212
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Book Description
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: Yu. E. Anikonov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110940906
Category : Mathematics
Languages : en
Pages : 280
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Book Description
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: I︠U︡riĭ Evgenʹevich Anikonov
Publisher: VSP
ISBN: 9789067643450
Category : Mathematics
Languages : en
Pages : 288
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Book Description
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: Yurii Ya. Belov
Publisher: Walter de Gruyter
ISBN: 3110944634
Category : Mathematics
Languages : en
Pages : 220
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Book Description
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
ISBN: 3110944987
Category : Mathematics
Languages : en
Pages : 244
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Book Description
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: Mikhail M. Lavrent'ev
Publisher: Walter de Gruyter
ISBN: 3110915529
Category : Mathematics
Languages : en
Pages : 288
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Book Description
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: Michael V. Klibanov
Publisher: Walter de Gruyter
ISBN: 3110915545
Category : Mathematics
Languages : en
Pages : 292
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Book Description
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: Vyacheslav I. Maksimov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110944839
Category : Mathematics
Languages : en
Pages : 280
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Book Description
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: Kenrick Bingham
Publisher: Springer Science & Business Media
ISBN: 3662089661
Category : Mathematics
Languages : en
Pages : 385
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Book Description
In inverse problems, the aim is to obtain, via a mathematical model, information on quantities that are not directly observable but rather depend on other observable quantities. Inverse problems are encountered in such diverse areas of application as medical imaging, remote sensing, material testing, geosciences and financing. It has become evident that new ideas coming from differential geometry and modern analysis are needed to tackle even some of the most classical inverse problems. This book contains a collection of presentations, written by leading specialists, aiming to give the reader up-to-date tools for understanding the current developments in the field.
Author: Vladimir G. Romanov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110943840
Category : Mathematics
Languages : en
Pages : 292
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Book Description
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.
