System of Singular Integral Equations in the Problem on Electromagnetic Oscillations of a Graphene-Coated Dielectric Ball

Background. Conjugate boundary value problems for a system of Maxwell’s equations are fundamental in electrodynamics. Recently, there has been interest in the problems involving the presence of a thin graphene layer on the surface, which changes the conjugation conditions. The aim of this study is to obtain a system of integral equations for the vector boundary value problem on electromagnetic oscillations of a graphene-coated dielectric ball in a spherical coordinate system. Materials and methods. Using the Stratton‒Chu formula, the components of the field are expressed through surface currents and the conjugation conditions are used to obtain singular integral equations on the ball surface. Results. A system of singular integral equations with four unknown scalar functions on the sphere surface is derived. The properties of the system of integral equations are studied. Conclusions. The resulting system of singular integral equations can be solved numerically by known methods, for example, the Galerkin method or the collocation method.