High-frequency asymptotics of time-periodic solutions to differential equations systems in a critical case
Abstract
For two linear evolution differential equations systems - a normal ordinary differential equations system and a partial differential equations system with Stokes operator in a main part - with rapidly oscillating by time coefficients in a case of an averaged stationary operator multiple degeneracy time-periodic solutions problem was considered. The results about their existence and uniqueness were proved and their asymptotic expansions were constructed and proved. Moreover, for normal ordinary differential equations system the convergence of the asymptotic expansion was proved in the ordinary meaning and Lyapunov's stability questions were investigated.
Keywords
Cite
@article{arxiv.1706.06055,
title = {High-frequency asymptotics of time-periodic solutions to differential equations systems in a critical case},
author = {Valeriy Borisovich Levenshtam and Linh Kop Nguyen and Marat Rashidovich Ishmeev},
journal= {arXiv preprint arXiv:1706.06055},
year = {2017}
}
Comments
in Russian. Keywords: linear normal differential equations system, Stokes operator, high-frequency oscillation of coefficients, averaging method, complete asymptotics, critical case, boundary layer method