### Abstract:

Mathematical modeling of thermophysical processes in an electric arc of high-current
disconnecting apparatuses leads to a boundary value problem for an essentially loaded heat conduction
equation. Taking into account the transience of such phenomena, in some cases only a mathematical
model is able to give adequate information about their dynamics. The mathematical model in the form
of the boundary value problem is reduced to the Volterra integral equation of the second kind, as a
result, we have that the solvability of the boundary value problem is equivalent to the solvability of the
reduced integral equation. Thus, there is a need to study the reduced integral equation. The results of
this study (various representations and properties of the kernel-forming function in general case and
the types of the kernel of the integral equation in special cases) are presented in this article. The article
is focused at physicists and engineers, as well as scientific researchers engaged in the practical
applications of loaded differential equations.