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Singularly Perturbed Cauchy Problem in Which the Limit Operator has Multiple Spectrum and a Weak First-Order Turning Point

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Abstract

Using S.A. Lomov’s regularization method, we construct an asymptotic solution of a linear Cauchy problem in which the limit operator has a weak turning point. The main singularities of the problem are written out explicitly. Estimates in \(\varepsilon \) characterizing the behavior of singularities as \(\varepsilon \to 0\) are given. The asymptotic convergence of regularized series is proved. The results are illustrated by an example.

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute”, Moscow, 111250, Russia

    A. G. Eliseev & P. V. Kirichenko

Authors
  1. A. G. Eliseev
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  2. P. V. Kirichenko
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Correspondence to A. G. Eliseev or P. V. Kirichenko.

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Translated by V. Potapchouck

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Eliseev, A.G., Kirichenko, P.V. Singularly Perturbed Cauchy Problem in Which the Limit Operator has Multiple Spectrum and a Weak First-Order Turning Point. Diff Equat 58, 727–740 (2022). https://doi.org/10.1134/S0012266122060027

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  • DOI: https://doi.org/10.1134/S0012266122060027

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