This article is cited in 9 papers

Mathematics

On the existence and uniqueness of solutions to the inverse boundary value problem for determining the effective permittivity of nanomaterials

Yu. G. Smirnov

Penza State University, Penza

Abstract: The paper is devoted to the problem of reconstruction of effective permittivity of nanomaterials of arbitrary shape located in rectangular waveguide with perfectly conducting walls. The problem is reduced to the nonlinear volume singular integral equation. Research of the integral equation is based on the theorem of equivalence of boundary value problem and integral equation. Theorem of existence and uniqueness of solutions of integral equation and boundary value problem for reconstruction of effective permittivity of nanomaterials is solved.

Keywords: inverse boundary value problems, integral equations, electromagnetic problems, theorems of existence and uniqueness of solutions.

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