Skip to main content
SpringerLink
Log in
Book cover

Integral Geometry and Inverse Problems for Hyperbolic Equations

  • Book
  • © 1974

Overview

Authors:
  1. V. G. Romanov

    1. Computer Center of the Academy of Science, Novosibirsk, USSR

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (4 chapters)

  1. Front Matter

    Pages I-VI
    Download chapter PDF

  2. Introduction

    • V. G. Romanov
    Pages 1-5

  3. Some Problems in Integral Geometry

    • V. G. Romanov
    Pages 6-52

  4. Inverse Problems for Hyperbolic Linear Differential Equations

    • V. G. Romanov
    Pages 53-126

  5. Application of the Linearized Inverse Kinematic Problem to Geophysics

    • V. G. Romanov
    Pages 127-147

  6. Back Matter

    Pages 148-154
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Computer Center of the Academy of Science, Novosibirsk, USSR

    V. G. Romanov

Bibliographic Information

  • Book Title: Integral Geometry and Inverse Problems for Hyperbolic Equations

  • Authors: V. G. Romanov

  • Series Title: Springer Tracts in Natural Philosophy

  • DOI: https://doi.org/10.1007/978-3-642-80781-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1974

  • Softcover ISBN: 978-3-642-80783-1Published: 19 January 2012

  • eBook ISBN: 978-3-642-80781-7Published: 09 April 2013

  • Series ISSN: 0081-3877

  • Edition Number: 1

  • Number of Pages: VI, 154

  • Topics: Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation