振荡Robin混合边值齐次化问题

数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 81-90.

振荡Robin混合边值齐次化问题

王娟*(),赵杰

中原工学院理学院郑州 451191

收稿日期:2020-03-18 出版日期:2021-02-26 发布日期:2021-01-29
通讯作者: 王娟 E-mail:wangjuan03022204@163.com
基金资助:
国家自然科学基金(11626239);河南省教育厅(18A110037);国家留学基金委(201708410483)

Homogenization of the Oscillating Robin Mixed Boundary Value Problems

Juan Wang*(),Jie Zhao

College of Science, Zhongyuan University of Technology, Zhengzhou 451191

Received:2020-03-18 Online:2021-02-26 Published:2021-01-29
Contact: Juan Wang E-mail:wangjuan03022204@163.com
Supported by:
Supported by the NSFC(11626239);the Education Department of Henan Province(18A110037);the CSC(201708410483)

摘要/Abstract

摘要：

该文研究了振荡Robin混合边值齐次化问题解的收敛率.该工作的困难之处在于Robin边值上出现的振荡因子以及边界交叉项的处理.该文利用对偶方法巧妙得对振荡积分进行了估计.文中建立了解的 $ H^{1}$和 $L^{2} $收敛率，所得结果明显地依赖于维数.该文可以视为将对偶方法和光滑算子，延拓到处理振荡Robin混合边值问题的情形.

关键词: 齐次化, 收敛率, 对偶方法, 光滑算子, 振荡积分

Abstract:

In this paper, we study the convergence rates of solutions for homogenization of the oscillating Robin mixed boundary value problems. The main difficulty of this work is due to the oscillating factor on the Robin boundary as well as boundary discrepancies. Thanks to the duality approach, we could handle the oscillatory integral. As a consequence, we establish the rates of convergence in $H^{1} $ and $L^{2} $, which depends on the dimension explicitly. This work may be regarded as an extension of the duality approach as well as smoothing operators for oscillating Robin mixed boundary value problems.

Key words: Homogenization, Convergence rates, Duality approach, Smoothing operators, Oscillatory integral

中图分类号:

O175.23

王娟,赵杰. 振荡Robin混合边值齐次化问题[J]. 数学物理学报, 2021, 41(1): 81-90.

Juan Wang,Jie Zhao. Homogenization of the Oscillating Robin Mixed Boundary Value Problems[J]. Acta mathematica scientia,Series A, 2021, 41(1): 81-90.

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