Existence and unicity of the solution of the diffraction problem for an electromagnetic wave on a system of non-intersecting bodies and screens

Background. The aim of this work is to theoretically study the vector problem of electromagnetic wave scattering by an obstacle of complex shape consisting of several solid bodies and infinitely thin absolutely conducting screens. Material and methods . The problem is considered in the quasiclassical statement (solution is sought in the classical sense everywhere except for the screen edge); to prove the theorem of uniqueness of the solution to the boundary value problem, the authors used classical integral formulas generalized for the elements of the Sobolev spaces; to prove existence and continuity of the solution, the researchers applied the theory of elliptic pseudodifferential operators over bounded manifolds. Results. The quasiclassical statement of the electromagnrtc wave diffraction problem has been suggested; the theorem of uniqueness of the quasi-classical solution to the boundary value problem was proved; the Fredholm property of the matrix integro-differential operator was established; the theorem on continuity of solutions to the integro-differential equations was proved. Conclusions. The obtained results can be used in the study of more complicated diffraction problems as well as for validation of numerical methods for their approximate solution.