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JOURNALS // Contemporary Mathematics. Fundamental Directions // Archive

CMFD, 2024 Volume 70, Issue 1, Pages 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

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.

UDC: 517.9

DOI: 10.22363/2413-3639-2024-70-1-53-76



© Steklov Math. Inst. of RAS, 2024