Averaging Method for Quasi-Linear Hyperbolic Systems

被引：0

作者：

Levenshtam, V. B. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Moscow, Russia

[2] Southern Fed Univ, Rostov Na Donu, Russia

来源：

RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS | 2023年 / 30卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

EQUATIONS;

D O I：

10.1134/S1061920823040118

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The paper considers the Cauchy problem for a multidimensional quasilinear hyperbolic system of differential equations with the data rapidly oscillating in time. This data do not explicitly depend on spatial variables. The method by N. M. Krylov-N. N. Bogolyubov is developed and justified for these systems. Also an algorithm is developed and justified, based on this method and the method of two-scale expansions, for constructing the complete asymptotics of solutions. DOI 10.1134/S1061920823040118

引用

页码：552 / 560

页数：9

共 18 条

[1]

Bogolyubov NikolayN., 1974, Asymptotic methods in the theory of nonlinear oscillations

[2] AN AVERAGING THEOREM FOR NONLINEAR SCHRODINGER EQUATIONS WITH SMALL NONLINEARITIES [J].

Huang, Guan .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (09) :3555-3574

[3]

Ivleva N, 2015, EURASIAN MATH J, V6, P41

[4]

Jian W., 2020, SMS, V75, P37

[5] On the Homogenization Principle in a Time-Periodic Problem for the Navier-Stokes Equations with Rapidly Oscillating Mass Force [J].

Khatskevich, V. L. .

MATHEMATICAL NOTES, 2016, 99 (5-6) :757-768

[6]

Khoma G. P., 1970, Ukr. math. magazine, V22, P699

[7]

Lehman B., 2002, IMA Journal of Mathematical Control and Information, V19, P201, DOI 10.1093/imamci/19.1_and_2.201

[8]

[Левешптам В.Б. Levenshtam V.B.], 2006, [Известия Российской академии наук. Серия математическая, Izvestiya: Mathematics, Izvestiya Rossiiskoi akademii nauk. Seriya matematicheskaya], V70, P25

[9]

Levenshtam V. B., 2010, Differential Equations with Large High-Frequency Components

[10] Higher-order approximations of the averaging method for parabolic initial-boundary value problems with rapidly oscillating coefficients [J].

Levenshtam, VB .

DIFFERENTIAL EQUATIONS, 2003, 39 (10) :1471-1479

← 1 2 →