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 Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 4, Pages 884–913 (Mi izv2497)

The construction of asymptotic solutions of certain problems involving parameters

S. A. Lomov

Abstract: In this article we present a theory for the construction of approximate solutions of certain differential equations involving parameters. The basic idea in this theory consists in removing the nonregular dependence of the solution on the parameter, by going to a space of higher dimension. We construct the asymptotic expansion of the solution to the problem regularized in this way, and establish a definite algorithm that allows us to construct the corresponding approximations for the original problem. The theory is presented by means of certain singularly perturbed nonlinear systems, and is applied to a nonhomogeneous problem with a “turning point.”

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English version:
Mathematics of the USSR-Izvestiya, 1968, 2:4, 849–877

Bibliographic databases:

UDC: 517.9
MSC: 41A60, 35R45, 35R20, 30E20

Citation: S. A. Lomov, “The construction of asymptotic solutions of certain problems involving parameters”, Izv. Akad. Nauk SSSR Ser. Mat., 32:4 (1968), 884–913; Math. USSR-Izv., 2:4 (1968), 849–877

Citation in format AMSBIB
\Bibitem{Lom68} \by S.~A.~Lomov \paper The construction of asymptotic solutions of certain problems involving parameters \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1968 \vol 32 \issue 4 \pages 884--913 \mathnet{http://mi.mathnet.ru/izv2497} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=237902} \zmath{https://zbmath.org/?q=an:0167.08301|0184.11901} \transl \jour Math. USSR-Izv. \yr 1968 \vol 2 \issue 4 \pages 849--877 \crossref{https://doi.org/10.1070/IM1968v002n04ABEH000675} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. P. Maslov, “Transition of the Heisenberg equation for $h\to 0$ to the dynamic equation of a monoatomic ideal gas and quantization of relativistic hydrodynamics”, Theoret. and Math. Phys., 1:3 (1969), 289–293
2. V. A. Trenogin, “The development and applications of the asymptotic method of Lyusternik and Vishik”, Russian Math. Surveys, 25:4 (1970), 119–156
3. S. A. Lomov, “The method of perturbations for singular problems”, Math. USSR-Izv., 6:3 (1972), 631–648
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