Investigation of electromagnetic wave diffraction from an inhomogeneous partially shielded solid

Abstract

Diffraction of electromagnetic wave from a partially shielded inhomogeneous dielectric is considered. The original boundary value problem for Maxwell’s equations is shown to have at most one quasi-classical solution. The problem is reduced to a system of integro-differential equations on the solid and the screens. The matrix integro-differential operator is treated in Sobolev spaces and is shown to be a continuously invertible operator. As a result, convergence of the Galerkin method is proved in the chosen functional spaces.

Keywords:

• Diffraction problem
• partially shielded solid
• Maxwell’s equations
• quasi-classical solution
• existence and uniqueness
• singular integro-differential equations
• invertible operator
• Galerkin method

AMS Subject Classifications:

• 35Q61
• 78A45
• 31B10
• 35S05
• 65M60

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Ministry of Education and Science of the Russian Federation [agreement No. 1.894.2017/4.6].