The regularized asymptotics of a solution of the Cauchy problem in the presence of a weak turning point of the limit operator

An asymptotic solution of the linear Cauchy problem in the presence of a ‘weak’ turning point of the limit operator is built using Lomov's regularization method. The major singularities of the problem are written out in an explicit form. Estimates are given with respect to $\varepsilon$, which characterise the behaviour of the singularities as $\varepsilon\to 0$. The asymptotic convergence of the regularized series is proved. The results of the work are illustrated by an example.
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