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Springer Tracts in Natural Philosophy

Integral Geometry and Inverse Problems for Hyperbolic Equations

Authors: Romanov, Vladimir

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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 reĀ­ 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.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-3-642-80781-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA in USD
  • ISBN 978-3-642-80783-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Integral Geometry and Inverse Problems for Hyperbolic Equations
Authors
Series Title
Springer Tracts in Natural Philosophy
Series Volume
26
Copyright
1974
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-80781-7
DOI
10.1007/978-3-642-80781-7
Softcover ISBN
978-3-642-80783-1
Series ISSN
0081-3877
Edition Number
1
Number of Pages
VI, 154
Topics

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