rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Inverse Problems
    sub title: Mathematical and Analytical Techniques with Applications to Engineering
  name:
    name part: Ramm, Alexander G.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2005
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 442 p. online resource.
  abstract: Inverse problems are the problems that consist of finding an unknown property of an object or a medium from the observation or a response of this object or a medium to a probing signal. Thus the theory of inverse problems yields a theoretical basis for remote sensing and non-destructive evaluation. For example, if an acoustic plane wave is scattered by an obstacle, and one observes the scattered field from the obstacle, or in some exterior region, then the inverse problem is to find the shape and material properties of the obstacle. Such problems are important in the identification of flying objects (airplanes, missiles etc.) objects immersed in water (submarines, fish) and in many other situations. This book presents the theory of inverse spectral and scattering problems and of many other inverse problems for differential equations in an essentially self-contained way. An outline of the theory of ill-posed problems is given, because inverse problems are often ill-posed. There are many novel features in this book. The concept of property C, introduced by the author, is developed and used as the basic tool for a study of a wide variety of one- and multi-dimensional inverse problems, making the theory easier and shorter. New results include recovery of a potential from I-function and applications to classical and new inverse scattering and spectral problems, study of inverse problems with"incomplete data", study of some new inverse problems for parabolic and hyperbolic equations, discussion of some non-overdetermined inverse problems, a study of inverse problems arising in the theory of ground-penetrating radars, development of DSM (dynamical systems method) for solving ill-posed nonlinear operator equations, comparison of the Ramm's inversion method for solving fixed-energy inverse scattering problem with the method based on the Dirichlet-to-Neumann map, derivation of the range of applicability and error estimates for Born's inversion, a study of some integral geomet…
  table of contents: Methods of Solving Ill-Posed Problems -- One-Dimensional Inverse Scattering and Spectral Problems -- Inverse Obstacle Scattering -- Stability of the Solutions to 3D Inverse Scattering Problems with Fixed-Energy Data -- Non-Uniqueness and Uniqueness Results -- Inverse Problems of Potential Theory and Other Inverse Source Problems -- Non-Overdetermined Inverse Problems -- Low-Frequency Inversion -- Wave Scattering by Small Bodies of Arbitrary Shapes -- The Pompeiu Problem.
  note: by Alexander G. Ramm.
  subject:
    topic: Engineering
  subject:
    topic: Image processing
  subject:
    topic: Differential equations
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Physics
  subject:
    topic: Engineering
  subject:
    topic: Appl.Mathematics/Computational Methods of Engineering
  subject:
    topic: Applications of Mathematics
  subject:
    topic: Theoretical, Mathematical and Computational Physics
  subject:
    topic: Image Processing and Computer Vision
  subject:
    topic: Ordinary Differential Equations
  classification: TA329-348
  classification: TA640-643
  classification: 519
  related item:
    title info:
      title: Springer eBooks
  identifier: 9780387232188
  identifier: http://dx.doi.org/10.1007/b100958
  record info:
    record creation date: 100301
    record change date: 20151204183020.0
    record identifier: 978-0-387-23218-8