{"title":"Averaging Method for Quasi-Linear Hyperbolic Systems","authors":"V.B. Levenshtam","doi":"10.1134/S1061920823040118","DOIUrl":null,"url":null,"abstract":"<p> 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. </p><p> <b> DOI</b> 10.1134/S1061920823040118 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"552 - 560"},"PeriodicalIF":1.7000,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920823040118","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
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.
摘要 本文研究了多维准线性双曲微分方程系统的 Cauchy 问题，其数据在时间上快速振荡。这些数据并不明确依赖于空间变量。由 N. M. Krylov-N.N. Bogolyubov 提出的方法，并对这些系统进行了论证。此外，基于该方法和双尺度展开法，还开发并论证了一种算法，用于构建解的完整渐近线。 doi 10.1134/s1061920823040118
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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