ON THE INFINITE FIELD OF A CLASS OF WEAKLY SINGULAR INTEGRAL EQUATIONS

Abstract

In this study, we present infinite field behaviors for a class of integral equations with weakly singular kernels (Abel type) based on the methods for integro-differential equations in paper [1]. This class of integro-differential equations originated from an aeroelasticity problem [2]. After taking derivatives on the integral equations, equations are in the form of integro-differential equations. By separating variables, choosing splines as basis, interchanging the differentiation and integration of the integro-differential parts, we are able to compute the infinite behaviors of solutions by steps and discover that the possible behaviors depend on a specific formation of the initial conditions. We conclude the main result as a theorem.