Integral Geometry And Inverse Problems For Hyperbolic Equations Nekotorye Obratnye Zada I Dlja Uravnenij Giperboli Eskogo Tipa Engl
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Integral Geometry And Inverse Problems For Hyperbolic Equations
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Author : V. G. Romanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Integral Geometry And Inverse Problems For Hyperbolic Equations written by V. G. Romanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
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.
Integral Geometry And Inverse Problems For Hyperbolic Equations
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Author : V. G Romanov
language : en
Publisher:
Release Date : 1974-07-23
Integral Geometry And Inverse Problems For Hyperbolic Equations written by V. G Romanov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-07-23 with categories.
Integral Geometry And Inverse Problems For Hyperbolic Equations
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Author : Vladimir Gavrilovich Romanov
language : en
Publisher: Springer
Release Date : 1974
Integral Geometry And Inverse Problems For Hyperbolic Equations written by Vladimir Gavrilovich Romanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Differential equations, Hyperbolic categories.
Direct Methods Of Solving Multidimensional Inverse Hyperbolic Problems
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Author : Sergey I. Kabanikhin
language : en
Publisher: Walter de Gruyter
Release Date : 2013-04-09
Direct Methods Of Solving Multidimensional Inverse Hyperbolic Problems written by Sergey I. Kabanikhin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
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.
Integral Geometry And Inverse Problems For Kinetic Equations
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Author : A. Kh Amirov
language : en
Publisher: VSP
Release Date : 2001
Integral Geometry And Inverse Problems For Kinetic Equations written by A. Kh Amirov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
In this monograph a new 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 subject of the book 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.This monograph will be of value and interest to mathematicians who deal with problems of integral geometry, direct and inverse problems of mathematical physics and geophysics and for specialists in computerized tomography.