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Integral Geometry and Inverse Problems for Hyperbolic Equations

  • V. G. Romanov

Part of the Springer Tracts in Natural Philosophy book series (STPHI, volume 26)

Table of contents

  1. Front Matter
    Pages I-VI
  2. V. G. Romanov
    Pages 1-5
  3. V. G. Romanov
    Pages 6-52
  4. Back Matter
    Pages 148-154

About this book

Introduction

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.

Keywords

Hyperbolic Equations Integral Integralgeometrie Partielle Differentialgleichung differential equation equation function space geometry

Authors and affiliations

  • V. G. Romanov
    • 1
  1. 1.Computer Center of the Academy of ScienceNovosibirskUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-80781-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1974
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-80783-1
  • Online ISBN 978-3-642-80781-7
  • Series Print ISSN 0081-3877
  • Buy this book on publisher's site