Integral Geometry and Inverse Problems for Hyperbolic Equations: 26 (Springer Tracts in Natural Philosophy) - Hardcover

Romanov, Vladimir

Hardcover

ISBN 10: 354006429X ISBN 13: 9783540064299

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1974

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.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1974
• Language: English
• ISBN 10: 354006429X
• ISBN 13: 9783540064299
• Binding: Hardcover
• Number of pages: 154