Abstract:
In this paper the regularization of a singularity with respect to a parameter is derived by means of an extension of the original operator and subsequent application of perturbation theory in an unbounded space, and used to solve an “extended” problem asymptotically. It is proved that this asymptotic solution is unique. An appropriate restriction of the asymptotic solution thus obtained will be an asymptotic solution of the original problem; this restriction is also unique. The theory of this method is illustrated by an example of an ordinary linear system of general form.
\Bibitem{Lom72}
\by S.~A.~Lomov
\paper The method of perturbations for singular problems
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 3
\pages 631--648
\mathnet{http://mi.mathnet.ru/eng/im2316}
\crossref{https://doi.org/10.1070/IM1972v006n03ABEH001893}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=330677}
\zmath{https://zbmath.org/?q=an:0273.34038}
Linking options:
https://www.mathnet.ru/eng/im2316
https://doi.org/10.1070/IM1972v006n03ABEH001893
https://www.mathnet.ru/eng/im/v36/i3/p635
This publication is cited in the following 6 articles:
Assiya Zhumanazarova, Young Im Cho, 2021 International Conference on Information and Communication Technology Convergence (ICTC), 2021, 477
Assiya Zhumanazarova, Young Im Cho, “Asymptotic Convergence of the Solution of a Singularly Perturbed Integro-Differential Boundary Value Problem”, Mathematics, 8:2 (2020), 213
M. Hazewinkel, Encyclopaedia of Mathematics, 1992, 197
S. A. Lomov, A. G. Eliseev, “Asymptotic integration of singularly perturbed problems”, Russian Math. Surveys, 43:3 (1988), 1–63
S. A. Lomov, A. S. Yudina, “The structure of a fundamental system of solutions of a singularly perturbed equation with a regular singular point”, Math. USSR-Izv., 21:2 (1983), 415–424
V. F. Safonov, “The regularization method for singularly perturbed systems of nonlinear differential equations”, Math. USSR-Izv., 14:3 (1980), 571–596
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