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BL
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| Record Number
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667479
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dltt
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| Main Entry
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Cakoni, Fioralba
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| Title & Author
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A qualitative approach to inverse scattering theory /\ Fioralba Cakoni, David Colton
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| Series Statement
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Applied Mathematical Sciences,; volume 188
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| Page. NO
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1 online resource (x, 297 pages) :: illustrations.
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| ISBN
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9781461488279 (electronic bk.)
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: 1461488273 (electronic bk.)
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9781461488262
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: 1461488265
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: 9781461488262
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| Bibliographies/Indexes
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Includes bibliographical references and index
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| Contents
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Functional Analysis and Sobolev Spaces -- Ill-Posed Problems -- Scattering by Imperfect Conductors -- Inverse Scattering Problems for Imperfect Conductors -- Scattering by Orthotropic Media -- Inverse Scattering Problems for Orthotropic Media -- Factorization Methods -- Mixed Boundary Value Problems -- Inverse Spectral Problems for Transmission Eigenvalues -- A Glimpse at Maxwell's Equations
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| Abstract
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Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms for solving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to the inverse scattering problem which avoids the incorrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques. These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties without making any weak scattering assumption and using essentially no a priori information on the nature of the scattering object
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| Subject
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Inverse scattering transform.
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Mathematics.
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Partial Differential Equations.
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Theoretical, Mathematical and Computational Physics.
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Fourier Analysis.
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| Dewey Classification
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515/.353
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| LC Classification
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QC20.7.S3
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| Added Entry
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Colton, David L.,1943-
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| Added Entry
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Ohio Library and Information Network.
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