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Regularized Solution of Singularly Perturbed Cauchy Problem in the Presence of Rational “Simple” Turning Point in Two-Dimensional Case
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Axiomatic Approach in the Analytic Theory of Singular Perturbations

Department of Mathematical Sciences, National Research University ”MPEI”, ul. Krasnokazarmennaya 14, 111250 Moscow, Russia
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 18 November 2019 / Revised: 17 December 2019 / Accepted: 25 December 2019 / Published: 16 January 2020
Introduced by S.A. Lomov, the concept of a pseudoanalytic (pseudoholomorphic) solution laid the foundation for the development of the singular perturbation analytical theory. In order for this concept to work in case of linear problems, an apparatus for the theory of exponential type vector spaces was developed. When considering nonlinear singularly perturbed problems, an algebraic approach is currently used. This approval is based on the properties of algebra homomorphisms for holomorphic functions with various numbers of variables, as a result of which it is possible to obtain pseudoholomorphic solutions. In this paper, formally singularly perturbed equations are considered in topological algebras, which allows the authors to formulate the main concepts of the singular perturbation analytical theory from the standpoint of maximal generality. View Full-Text
Keywords: ε-regular function; invariants of equations and systems; ε-pseudoregular solution; essentially singular manifold ε-regular function; invariants of equations and systems; ε-pseudoregular solution; essentially singular manifold
MDPI and ACS Style

Besova, M.; Kachalov, V. Axiomatic Approach in the Analytic Theory of Singular Perturbations. Axioms 2020, 9, 9.

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