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Ill-Posed Problems of Mathematical Physics and Analysis
M. M. Lavrent'ev, V. G. Romanov, and S. P. Shishatskiĭ
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Translations of Mathematical Monographs
1986; 290 pp; softcover
Volume: 64
Reprint/Revision History:
thrid printing 2000
ISBN-10: 0-8218-0896-6
ISBN-13: 978-0-8218-0896-2
List Price: US$100
Member Price: US$80
Order Code: MMONO/64.S
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In this book the authors present a number of examples which lead to ill-posed problems arising with the processing and interpretation of data of physical measurements. Basic postulates and some results in the general theory of ill-posed problems follow. The exposition also includes problems of analytic continuation from continua and discrete sets, analogous problems of continuation of solutions of elliptic and parabolic equations, the main ill-posed boundary value problem for partial differential equations, and results on the theory of Volterra equations of the first kind. A very broad presentation is given of modern results on the problem of uniqueness in integral geometry and on inverse problems for partial differential equations.

Readership

Table of Contents

  • Physical formulations leading to ill-posed problems
  • Basic concepts of the theory of ill-posed problems
  • Analytic continuation
  • Boundary value problems for differential equations
  • Volterra equations
  • Integral geometry
  • Multidimensional inverse problems for linear differential equations
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