To the solution of the singular inhomogeneous integral Volterra equation

Abstract

In the article the inhomogeneous singular Volterra integral equation of the second kind is investigated, to which the boundary value problem of heat conduction is reduced, that arises at solving some problems with free boundaries. A general solution of this equation is found that represents the sum of the general solution to the homogeneous equation and the particular solution to the inhomogeneous equation. An estimate of the constructed resolvent for the integral equation is given.