Regularized Asymptotic Solutions of Singularly Perturbed Integral Equations with a Higher-Order Diagonal Degeneration of the Kernel and the Initialization Problem

摘要

An algorithm of the regularization method is developed for singularly perturbed integral equations with a higher-order diagonal degeneration of the kernel. The leading term of the asymptotics is analyzed to solve the problem of initialization (that is, extraction of the class of right-hand sides and kernels of the integral operator for which the exact solution of the original equation tends to some limit function as epsilon -> +0 on the entire time interval, including the boundary-layer zone).