Integral geometry and inverse problems for hyperbolic equations (Nekotorye obratnye zadači dlja uravnenij giperboličeskogo tipa, engl.) PDF Download
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Author: Vladimir G. Romanov
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Vladimir G. Romanov
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: V. G. Romanov
Publisher: Springer Science & Business Media
ISBN: 364280781X
Category : Mathematics
Languages : en
Pages : 160
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Book Description
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.
Author: V. G Romanov
Publisher:
ISBN: 9783642807824
Category :
Languages : en
Pages : 164
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Author: Vladimir Gavrilovich Romanov
Publisher: Springer
ISBN: 9780387064291
Category : Differential equations, Hyperbolic
Languages : en
Pages : 0
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Book Description
Author: Sergey I. Kabanikhin
Publisher: Walter de Gruyter
ISBN: 3110960710
Category : Mathematics
Languages : en
Pages : 188
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Book Description
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.
Author: V. G. Romanov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110926016
Category : Mathematics
Languages : en
Pages : 248
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Book Description
No detailed description available for "Inverse Problems of Mathematical Physics".
Author: M. M. Lavrentiev
Publisher: Lecture Notes in Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 72
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Book Description
Author: Mikhail M. Lavrent'ev
Publisher: Walter de Gruyter
ISBN: 9789067643962
Category : Mathematics
Languages : en
Pages : 296
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Book Description
Thismonograph deals with the theory of inverse problems of mathematical physics andapplications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.
