On the regularized asymptotics of a solution to the cauchy problem in the presence of a weak turning point of the limit operator

Abstract

An asymptotic solution of the linear Cauchy problem in the presence of a "weak" turning point for the limit operator is constructed by the method of S. A. Lomov regularization. The main singularities of this problem are written out explicitly. Estimates are given for ε that characterize the behavior of singularities for ε → 0. The asymptotic convergence of a regularized series is proven. The results are illustrated by an example. Bibliography: six titles.