Integral geometry inverse problems (43 Ergebnisse)

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Hardcover. Zustand: Sehr gut. Bln., Springer 1974. VI, 151 p. OCloth. Springer Tracts in Natural Philosophy, 26.- In very good condition.

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.…

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Zustand: gut. 1974. Integral Geometry and Inverse Problems for Hyperbolic Equations. (= Springer Tracts in Natural Philosophy, Volume 26). In deutscher Sprache. pages.

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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.…

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