Mathematics

Problem of electromagnetic wave diffraction on homogeneous dielectric ball coated with graphene

Yu. G. Smirnov, O. V. Kondyrev

Penza State University, Penza

Abstract: Background. Boundary value problems for Maxwell's equations are widely used in various fields of electrodynamics due to their ability to model complex physical situations associated with the interaction of electromagnetic waves with boundaries and thin layers of materials. The objective of this work is to derive and analyze a system of integral equations for the problem of electromagnetic wave diffraction on a dielectric ball coated with graphene, and to prove the existence and uniqueness of a solution to the boundary value problem. Materials and methods. Using a combination of Stratton-Chu formulas, a system of vector integral equations over the surface of a sphere is obtained. Results. A system of scalar singular integral equations is obtained for searching for four unknown functions. The theorem on the existence and uniqueness of the solution of the system of equations, as well as the existence and uniqueness of the solution of the boundary value problem of diffraction is proved. Conclusions. The problem of electromagnetic wave diffraction on a dielectric ball coated with graphene has been studied, and a system of equations for numerical solution has been obtained.

Keywords: singular integral equation, Maxwell equations, dielectric body, graphene

UDC: 517.3

DOI: 10.21685/2072-3040-2025-2-5