高阶方程混合边界齐次化问题

数学物理学报 ›› 2020, Vol. 40 ›› Issue (4): 925-933.

高阶方程混合边界齐次化问题

王娟*(),赵杰

^{中原工学院理学院郑州 451191}

收稿日期:2019-04-23 出版日期:2020-08-26 发布日期:2020-08-20
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(201708410483)

Homogenization of Higher-Order Equations with Mixed Boundary Condition

Juan Wang*(),Jie Zhao

^{College of Science, Zhongyuan University of Technology, Zhengzhou 451191}

Received:2019-04-23 Online:2020-08-26 Published:2020-08-20
Contact: Juan Wang E-mail:wangjuan03022204@163.com
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2m阶椭圆方程在Dirichlet-Neumann混合边界条件下的齐次化问题解的收敛率.文中主要使用了光滑算子，这就避免了对混合边界重叠项进行估计.该文建立了$H_{0}^{m}$和$L^{2}$空间下的收敛率估计.该项工作还将光滑算子的使用推广到了高阶方程混合边界条件的情形.

关键词: 齐次化, 高阶方程, 收敛率, 混合边界条件

Abstract:

The paper is concerned with the convergence rates of solutions for homogenization of m$-order elliptic equations with the mixed Dirichlet-Neumann boundary conditions. Our approach, which involves smoothing operator and thus avoids the estimates of the boundary discrepancies terms. As a consequence, we establish the rates of convergence in $H_{0}^{m}$ as well as $L^{2}$. This work may be regarded as an extension of the usage smoothing operator to the case of higher-order equations with mixed boundary condition settings.

Key words: Homogenization, Higher-order equations, Convergence rates, Mixed boundary condition

中图分类号:

O175.23

王娟,赵杰. 高阶方程混合边界齐次化问题[J]. 数学物理学报, 2020, 40(4): 925-933.

Juan Wang,Jie Zhao. Homogenization of Higher-Order Equations with Mixed Boundary Condition[J]. Acta mathematica scientia,Series A, 2020, 40(4): 925-933.

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