Problems of restoring sources from boundary observations in the quasi-stationary approximation for the system of Maxwell equations

A. V. Kalinin, A. A. Tyukhtina

Lobachevski State University of Nizhni Novgorod

Abstract: In this paper, we consider various formulations of boundary-value problems on determining time-periodic electromagnetic fields and their sources in conducting domains for the system of Maxwell equations in the quasi-stationary electromagnetic approximation. For various versions of boundary conditions corresponding to the assignment of tangential and normal components of electric and magnetic fields on the boundary of the considered spatial domain, we characterize the spaces of sources the projections onto which are uniquely restored by these boundary conditions.

Keywords: Maxwell equations, quasi-stationary approximation, inverse source problem, boundary observation, orthogonal projection

UDC: 517.958

MSC: 35Q61

DOI: 10.36535/2782-4438-2025-244-55-68