Integral Geometry and Inverse Problems for Hyperbolic Equations

V. G. Romanov

ISBN 10: 3642807836 / ISBN 13: 9783642807831

Published by Springer Berlin Heidelberg, Springer Berlin Heidelberg Jan 2012, 2012

About this Item

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 164 pp. Englisch.

Seller Inventory # 9783642807831

Bibliographic Details

• Title: Integral Geometry and Inverse Problems for Hyperbolic Equations
• Publisher: Springer Berlin Heidelberg, Springer Berlin Heidelberg Jan 2012
• Publication Date: 2012
• Language: English
• ISBN 10: 3642807836
• ISBN 13: 9783642807831
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 244W x 156H x 10D millimeters 244 millimeters width by 156 millimeters height by 10 millimeters depth
• Weight: 271 grams

About this title

Synopsis

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.