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Contemporary Mathematics. Fundamental Directions, 2024, Volume 70, Issue 1, Pages 53–76
DOI: https://doi.org/10.22363/2413-3639-2024-70-1-53-76 (Mi cmfd529) 		 
Averaging method for problems on quasiclassical asymptotics

S. Yu. Dobrokhotovab, V. E. Nazaikinskiiba

a Ishlinsky Institute for Problems in Mechanics of the RAS, Moscow, Russia
b Centre of Integrable Systems, P. G. Demidov Yaroslavl State University, Yaroslavl, Russia
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DOI: https://doi.org/10.22363/2413-3639-2024-70-1-53-76
Abstract: The averaging method is developed for operators with rapidly oscillating coefficients, intended for use in problems of quasiclassical asymptotics and not assuming a periodic structure of coefficient oscillations. Algebras of locally averaged functions are studied, an averaging theorem for differential operators of general form is proved, and some features of the method are illustrated using the example of the wave equation.
Keywords: averaging methods, rapidly oscillating coefficients, quasiclassical asymptotics, algebras of locally averaged functions.
Funding agency Grant number
Russian Science Foundation 21-71-30011
The research was supported by the grant of the Russian Science Foundation (project № 21-71-30011).
English version:
Journal of Mathematical Sciences, 2024, Volume 286, Issue 1, Pages 46–67
DOI: https://doi.org/10.1007/s10958-024-07490-6
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Averaging method for problems on quasiclassical asymptotics”, Functional spaces. Differential operators. Problems of mathematics education, CMFD, 70, no. 1, PFUR, M., 2024, 53–76; Journal of Mathematical Sciences, 286:1 (2024), 46–67
Citation in format AMSBIB
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\by S.~Yu.~Dobrokhotov, V.~E.~Nazaikinskii
\paper Averaging method for problems on quasiclassical asymptotics
\inbook Functional spaces. Differential operators. Problems of mathematics education
\serial CMFD
\yr 2024
\vol 70
\issue 1
\pages 53--76
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd529}
\crossref{https://doi.org/10.22363/2413-3639-2024-70-1-53-76}
\edn{https://elibrary.ru/YPMUOA}
\transl
\jour Journal of Mathematical Sciences
\yr 2024
\vol 286
\issue 1
\pages 46--67
\crossref{https://doi.org/10.1007/s10958-024-07490-6}
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