On the existence and uniqueness of solutions of the inverse boundary value problem for determining the permittivity of materials

On the existence and uniqueness of solutions of the inverse boundary value problem for determining the permittivity of materials

The problem of determining the permittivity of material samples of arbitrary shape placed in a rectangular waveguide with perfectly conducting walls is investigated. The problem is reduced to solving a nonlinear volume singular integral equation. A theorem on the existence and uniqueness of solution...

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Veröffentlicht in:Computational mathematics and mathematical physics 2010-09, Vol.50 (9), p.1511-1521
Hauptverfasser: Mironov, D. A., Smirnov, Yu. G.
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Boundary value problems
Composite materials
Computational mathematics
Computational Mathematics and Numerical Analysis
Dielectric constant
Integral equations
Inverse
Inverse problems
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinearity
Permittivity
Singular integral equations
Studies
Theorems
Uniqueness
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Beschreibung
Zusammenfassung:The problem of determining the permittivity of material samples of arbitrary shape placed in a rectangular waveguide with perfectly conducting walls is investigated. The problem is reduced to solving a nonlinear volume singular integral equation. A theorem on the existence and uniqueness of solutions to the nonlinear volume singular integral equation and of the inverse boundary value problem for determining the permittivity of the material is proved.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542510090046