In a cycle of papers, published especially in Russian beginning in 1990, the author studied the solvability of some dynamic problems for elastic media, using potential theory methods. In this paper, he analyses the same problem in electromagnetics and he announces that this is the first one from a more comprehensive cycle. The methods used by him were suggested by A. Bamberger and T. Ha Duong in two papers [Math. Methods Appl. Sci. 8, 598-608 (1986; Zbl 0636.65119), ibid., 405-435 (1986; Zbl 0618.35069)].
The author proceeds as follows: He eliminates from the Maxwell system the magnetic field, and for the electric field the problem reduces to the boundary value problem \[ \partial^2_t E(X)-a^2\Delta E(X)=0,\quad X\in G^\pm, \] with the initial conditions \(E(x+0)=\partial_tE(x+0)\), \(x\in\Omega^\pm\). Searching the fundamental solution for the equation \[ (\partial^2_t- a^2\Delta)\Phi(X)= \delta(X), \] he introduces two potentials of single and double-layer on the surface \(\Sigma= S\times \mathbb{R}\) of \(\Omega\). The limiting transition of an interior or exterior point of \(\Omega\) to the boundary surface yields a system of boundary integral equations for which the author proves the unique solvability in some Sobolev space.