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Inverse obstacle scattering with non...
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Ramm, A. G.
Inverse obstacle scattering with non-over-determined scattering data /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Inverse obstacle scattering with non-over-determined scattering data // Alexander G. Ramm.
作者:
Ramm, A. G.
面頁冊數:
1 PDF (xv, 53 pages).
附註:
Part of: Synthesis digital library of engineering and computer science.
標題:
Inverse problems (Differential equations) - Numerical solutions. -
電子資源:
https://doi.org/10.2200/S00925ED1V01Y201905MAS027
電子資源:
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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Inverse obstacle scattering with non-over-determined scattering data /
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Alexander G. Ramm.
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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
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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
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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.
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Compendex
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510
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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
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Also available in print.
538
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Mode of access: World Wide Web.
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System requirements: Adobe Acrobat Reader.
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Title from PDF title page (viewed on June 26, 2019).
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528131
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Scattering (Mathematics)
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direct scattering
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inverse obstacle scattering
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numerical analysis
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Abstract with links to resource
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