临界情形下微分方程组时间周期解的高频渐近
偏微分方程分析
2017-06-20 v1
摘要
针对两个线性演化微分方程组——一个正规常微分方程组和一个主部含 Stokes 算子的偏微分方程组——在系数随时间快速振荡且平均定常算子发生多重退化情形下，研究了其时间周期解问题。证明了其存在性与唯一性结果，并构造和证明了其渐近展开。此外，对于正规常微分方程组，证明了渐近展开在通常意义下的收敛性，并研究了 Lyapunov 稳定性问题。
引用
@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}
}
备注
in Russian. Keywords: linear normal differential equations system, Stokes operator, high-frequency oscillation of coefficients, averaging method, complete asymptotics, critical case, boundary layer method