Regularization of nonlinear Volterra integral equations of the first kind in a generalized sense

Abstract

This paper investigates an ill-posed nonlinear Volterra integral equation of the first kind. In order to study the original integral equation and to prove its regularizability in the class of generalized functions, the method of integral operators with the use of auxiliary functions is applied, as well as an asymptotic regularization algorithm containing a singular function with respect to a small parameter.
It should be noted that the considered Volterra integral equation of the first kind degenerates in inverse problems arising in the theory of moisture transfer, hereditary media, and other applied fields, which determines the actuality of this paper.

Key Words: Volterra integral equation of the first kind (VIE-1), regularization method (RM),
uniqueness of solution, regularizability in the generalized sense.