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Inverse obstacle scattering with non-over-determined scattering data /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Inverse obstacle scattering with non-over-determined scattering data // Alexander G. Ramm.
Author:	Ramm, A. G.
Description:	1 PDF (xv, 53 pages).
Notes:	Part of: Synthesis digital library of engineering and computer science.
Subject:	Inverse problems (Differential equations) - Numerical solutions. -
Online resource:	https://doi.org/10.2200/S00925ED1V01Y201905MAS027
Online resource:	https://ieeexplore.ieee.org/servlet/opac?bknumber=8736534
ISBN:	9781681735894

Inverse obstacle scattering with non-over-determined scattering data /
Ramm, A. G.

Inverse obstacle scattering with non-over-determined scattering data /Alexander G. Ramm. - 1 PDF (xv, 53 pages). - Synthesis lectures on mathematics and statistics,#271938-1751 ;. - Synthesis digital library of engineering and computer science..

Part of: Synthesis digital library of engineering and computer science.

Includes bibliographical references (pages 49-51).

1 Introduction -- 2 The direct scattering problem -- 2.1 Statement of the problem -- 2.2 Uniqueness of the scattering solution -- 2.3 Existence of the scattering solution -- 2.4 Properties of the scattering amplitude

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

Compendex

The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering [alpha]([beta];[alpha];[kappa]), where [alpha]([beta];[alpha];[kappa]) is the scattering amplitude, [beta];[alpha][epsilon] S2 is the direction of the scattered, incident wave, respectively, S2 is the unit sphere in the R3 and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensionality one understands the minimal number of variables of a function describing the data or an object. In an inverse obstacle scattering problem this number is 2, and an example of non-over-determined data is [alpha]([beta]) := [alpha]([beta];[alpha]0;[beta]0). By sub-index 0 a fixed value of a variable is denoted. It is proved in this book that the data [alpha]([beta]), known for all [beta] in an open subset of S2, determines uniquely the surface S and the boundary condition on S. This condition can be the Dirichlet, or the Neumann, or the impedance type. The above uniqueness theorem is of principal importance because the non-over-determined data are the minimal data determining uniquely the unknown S. There were no such results in the literature, therefore the need for this book arose. This book contains a self-contained proof of the existence and uniqueness of the scattering solution for rough surfaces.

Mode of access: World Wide Web.

ISBN: 9781681735894

Standard No.: 10.2200/S00925ED1V01Y201905MAS027doiSubjects--Topical Terms:

528131
Inverse problems (Differential equations)
--Numerical solutions.Subjects--Index Terms:

direct scattering

LC Class. No.: QA377 / .R365 2019eb

Dewey Class. No.: 515/.352

Inverse obstacle scattering with non-over-determined scattering data /
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020 $z 9781681735900 $q hardcover
020 $z 9781681735887 $q paperback
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050 4 $a QA377 $b .R365 2019eb
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100 1 $a Ramm, A. G. $q (Alexander G.), $e author. $3 1253115
245 1 0 $a Inverse obstacle scattering with non-over-determined scattering data / $c Alexander G. Ramm.
264 1 $a [San Rafael, California] : $b Morgan & Claypool, $c 2019.
300 $a 1 PDF (xv, 53 pages).
336 $a text $2 rdacontent
337 $a electronic $2 isbdmedia
338 $a online resource $2 rdacarrier
490 1 $a Synthesis lectures on mathematics and statistics, $x 1938-1751 ; $v #27
500 $a Part of: Synthesis digital library of engineering and computer science.
504 $a Includes bibliographical references (pages 49-51).
505 0 $a 1 Introduction -- 2 The direct scattering problem -- 2.1 Statement of the problem -- 2.2 Uniqueness of the scattering solution -- 2.3 Existence of the scattering solution -- 2.4 Properties of the scattering amplitude
505 8 $a 3 Inverse obstacle scattering -- 3.1 Statement of the problem -- 3.2 Uniqueness of the solution to obstacle inverse scattering problem with the data a([beta]) -- 3.3 Uniqueness of the solution to the inverse obstacle scattering problem with fixed-energy data -- 3.4 Uniqueness of the solution to inverse obstacle scattering problem with non-over-determined data -- 3.5 Numerical solution of the inverse obstacle scattering problem with non-over-determined data
505 8 $a A. existence and uniqueness of the scattering solutions in the exterior of rough domains -- A.1. Introduction -- A.2. Uniqueness theorem -- A.3. Existence of the scattering solutions for compactly supported potentials -- A.4. Existence of the scattering solution for decaying potentials.
506 $a Abstract freely available; full-text restricted to subscribers or individual document purchasers.
510 0 $a Compendex
510 0 $a INSPEC
510 0 $a Google scholar
510 0 $a Google book search
520 $a The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering [alpha]([beta];[alpha];[kappa]), where [alpha]([beta];[alpha];[kappa]) is the scattering amplitude, [beta];[alpha][epsilon] S2 is the direction of the scattered, incident wave, respectively, S2 is the unit sphere in the R3 and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensionality one understands the minimal number of variables of a function describing the data or an object. In an inverse obstacle scattering problem this number is 2, and an example of non-over-determined data is [alpha]([beta]) := [alpha]([beta];[alpha]0;[beta]0). By sub-index 0 a fixed value of a variable is denoted. It is proved in this book that the data [alpha]([beta]), known for all [beta] in an open subset of S2, determines uniquely the surface S and the boundary condition on S. This condition can be the Dirichlet, or the Neumann, or the impedance type. The above uniqueness theorem is of principal importance because the non-over-determined data are the minimal data determining uniquely the unknown S. There were no such results in the literature, therefore the need for this book arose. This book contains a self-contained proof of the existence and uniqueness of the scattering solution for rough surfaces.
530 $a Also available in print.
538 $a Mode of access: World Wide Web.
538 $a System requirements: Adobe Acrobat Reader.
588 $a Title from PDF title page (viewed on June 26, 2019).
650 0 $a Inverse problems (Differential equations) $x Numerical solutions. $3 528131
650 0 $a Scattering (Mathematics) $3 527747
653 $a direct scattering
653 $a inverse obstacle scattering
653 $a numerical analysis
653 $a mathematical analysis
653 $a non-over-determined data
776 0 8 $i Print version: $z 9781681735887 $z 9781681735900
830 0 $a Synthesis digital library of engineering and computer science. $3 598254
830 0 $a Synthesis lectures on mathematics and statistics ; $v #26. $3 1253098
856 4 0 $3 Abstract with links to full text $u https://doi.org/10.2200/S00925ED1V01Y201905MAS027
856 4 2 $3 Abstract with links to resource $u https://ieeexplore.ieee.org/servlet/opac?bknumber=8736534