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Open AccessArticle

Regularized Solution of Singularly Perturbed Cauchy Problem in the Presence of Rational “Simple” Turning Point in Two-Dimensional Case

by Alexander Eliseev †,‡ and Tatjana Ratnikova *,‡
Research Group on Macro-Structural Modeling of the Russian Economy, National Research University ”MPEI”, 111250 Moscow, Russia
*
Author to whom correspondence should be addressed.
Current address: National Research University ”MPEI”, Kracnokazarmennaya st., 14, 111250 Moscow, Russia.
These authors contributed equally to this work.
Axioms 2019, 8(4), 124; https://doi.org/10.3390/axioms8040124
Received: 17 September 2019 / Revised: 28 October 2019 / Accepted: 30 October 2019 / Published: 1 November 2019
By Lomov’s S.A. regularization method, we constructed an asymptotic solution of the singularly perturbed Cauchy problem in a two-dimensional case in the case of violation of stability conditions of the limit-operator spectrum. In particular, the problem with a ”simple” turning point was considered, i.e., one eigenvalue vanishes for t = 0 and has the form t m / n a ( t ) (limit operator is discretely irreversible). The regularization method allows us to construct an asymptotic solution that is uniform over the entire segment [ 0 , T ] , and under additional conditions on the parameters of the singularly perturbed problem and its right-hand side, the exact solution. View Full-Text
Keywords: singularly perturbed Cauchy problem; regularized asymptotic solution; rational ”simple” turning point singularly perturbed Cauchy problem; regularized asymptotic solution; rational ”simple” turning point
MDPI and ACS Style

Eliseev, A.; Ratnikova, T. Regularized Solution of Singularly Perturbed Cauchy Problem in the Presence of Rational “Simple” Turning Point in Two-Dimensional Case. Axioms 2019, 8, 124.

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