ON EXISTENCE AND UNIQUENESS OF THE INVERSE BOUNDARY VALUE PROBLEM SOLUTION FOR IDENTIFYING EFFECTIVE DIELECTRIC PERMEABILITY OF NANOMATERIALS 

Smirnov Yury Gennadyevich, Doctor of Science (in Mathematics), professor, head of sub-department of mathematics and supercomputer modeling, Penza State University

517.6+537.874.6

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.

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