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Existence and uniqueness of solution to the inverse problem of complex permittivity reconstruction of a dielectric body in a waveguide
Karlstad University, Faculty of Technology and Science, Department of Mathematics. (Surface Treatment Program/T2F)ORCID iD: 0000-0002-2691-2820
Russia.
2010 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 26, no 10Article in journal (Refereed) Published
Abstract [en]

This paper presents a statement, a proof of uniqueness, and a method of solution to the inverse problem of the determination of permittivity of a lossy dielectric inclusion in a three-dimensional waveguide of rectangular cross-section fromthe transmission characteristics. The approach is based on the solution to a volume singular integral equation (VSIE). The examination of this equationis based on the analysis of the corresponding boundary value problem (BVP) for the system of Maxwell equations and the equivalence of this BVP andVSIE. The existence and uniqueness for VSIE in the space of square-integrable functions are proved. The permittivity reconstruction employs a method ofiterations applied to the solution of VSIE

Place, publisher, year, edition, pages
Bristol: IoP , 2010. Vol. 26, no 10
Keyword [en]
singular integral equation, waveguide, permittivity
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-10032DOI: 10.1088/0266-5611/26/10/105002ISI: 000282068000002OAI: oai:DiVA.org:kau-10032DiVA: diva2:493549
Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2016-06-09Bibliographically approved

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Publisher's full texthttp://iopscience.iop.org/0266-5611/26/10/105002/pdf/0266-5611_26_10_105002.pdf

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