Solution of a Singular Integral Equation of Volterra Type of the Second Kind

The article presents a general solution to the singular Volterra integral equation of the second kind. A distinctive feature of the integral equation under consideration is that the integral of its kernel does not equal zero as the upper limit approaches the lower one; therefore, the Picard method is not applicable. It is demonstrated that the corresponding homogeneous integral equation has a non-zero solution, which is explicitly found. Such integral equations typically arise, for example, in boundary problems of heat conduction in degenerating domains, the boundaries of which change with time. They are also relevant to problems in mathematical modeling of thermophysical processes in the electric arcs of high-current circuit breakers.