Existence and uniqueness of solution to the inverse problem of complex permittivity reconstruction of a dielectric body in a waveguide

• 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

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

singular integral equation

waveguide

permittivity

Matematik

Mathematics

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