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Titlebook: Integral Geometry and Inverse Problems for Hyperbolic Equations; V. G. Romanov Book 1974 Springer-Verlag Berlin Heidelberg 1974 Hyperbolic

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书目名称Integral Geometry and Inverse Problems for Hyperbolic Equations
编辑V. G. Romanov
视频video
丛书名称Springer Tracts in Natural Philosophy
图书封面Titlebook: Integral Geometry and Inverse Problems for Hyperbolic Equations;  V. G. Romanov Book 1974 Springer-Verlag Berlin Heidelberg 1974 Hyperbolic
描述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.
出版日期Book 1974
关键词Hyperbolic Equations; Integral; Integralgeometrie; Partielle Differentialgleichung; differential equatio
版次1
doihttps://doi.org/10.1007/978-3-642-80781-7
isbn_softcover978-3-642-80783-1
isbn_ebook978-3-642-80781-7Series ISSN 0081-3877
issn_series 0081-3877
copyrightSpringer-Verlag Berlin Heidelberg 1974
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Some Problems in Integral Geometry,Consider the following problem in (. + 1)-dimensional space (. ≥ 1): The integrals of a function .(.)=.(.,...,., .) are known over a family of ellipsoids of revolution with one focus fixed at the origin and the other running over a point set of the hyperplane . = 0. Determine the function .(., .) from the known integrals.
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Springer Tracts in Natural Philosophyhttp://image.papertrans.cn/i/image/468309.jpg
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https://doi.org/10.1007/978-3-642-80781-7Hyperbolic Equations; Integral; Integralgeometrie; Partielle Differentialgleichung; differential equatio
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Introduction,nown 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 s
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Inverse Problems for Hyperbolic Linear Differential Equations,e of the type . Here .(.) is the unknown function, . = (.,...,.) is a fixed point and . = (.,...,.) a variable point of .,...,. space .(. - ., .) is Dirac’s delta function [27] and L the elliptic differential operator..
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Application of the Linearized Inverse Kinematic Problem to Geophysics,the inhomogeneous structure of the Earth. The numerical solution of the problem is described in a slightly simplified form and a number of numerical computer experiments performed with the aid of this technique are discussed.
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