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<p>In this paper, based on S. A. Lomov’s regularization method, we construct an asymptotic solution of a singularly perturbed Cauchy problem in the case of violation of the stability conditions for the spectrum of the limit operator. In particular, we consider the problem with a “simple” turning point, i.e., where one eigenvalue vanishes for <i>t</i> = 0 and has the form <i>t</i><sup><i>m/n</i></sup> (the limit operator is discretely irreversible).</p>

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Asymptotic Solution of a Singularly Perturbed Cauchy Problem in the Presence of a Rational Simple Turning Point

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • A. G. Eliseev,
  • T. A. Ratnikova

摘要

In this paper, based on S. A. Lomov’s regularization method, we construct an asymptotic solution of a singularly perturbed Cauchy problem in the case of violation of the stability conditions for the spectrum of the limit operator. In particular, we consider the problem with a “simple” turning point, i.e., where one eigenvalue vanishes for t = 0 and has the form tm/n (the limit operator is discretely irreversible).