Averaging method for problems on quasiclassical asymptotics

S. Yu. Dobrokhotov ; V. E. Nazaikinskii

Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 1, pp. 53-76.

Résumé

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.

Détail

Keywords: averaging methods, rapidly oscillating coefficients, quasiclassical asymptotics, algebras of locally averaged functions.

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