Homogenization of a mixed boundary condition

被引：2

作者：

Marusic-Paloka, Eduard ^{[1
]}

Pazanin, Igor ^{[1
]}

机构：

[1] Univ Zagreb, Fac Sci, Dept Math, Zagreb, Croatia

来源：

APPLICABLE ANALYSIS | 2022年 / 101卷 / 12期

关键词：

Periodic boundary condition; homogenization; boundary layer; Laplace equation; the Zaremba problem; LAPLACIAN;

D O I：

10.1080/00036811.2022.2027383

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the asymptotic behavior of the periodically mixed boundary value problem. The Dirichlet and Neumann boundary conditions are non-homogeneous and periodically mixed with small period epsilon. Using asymptotic analysis with respect to epsilon << 1, wederive an asymptotic approximation that has boundary condition of the Robin type. We justify the obtained condition by proving an appropriate error estimate.

引用

页码：4113 / 4125

页数：13

共 23 条

[1] HOMOGENIZATION AND 2-SCALE CONVERGENCE [J].

ALLAIRE, G .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1992, 23 (06) :1482-1518

[2]

Allaire G., 1996, P INT C MATH MOD FLO, P1525

[3]

[Anonymous], 1993, MAT SB

[4] Homogenization in a thin domain with an oscillatory boundary [J].

Arrieta, Jose M. ;

Pereira, Marcone C. .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2011, 96 (01) :29-57

[5]

Bakhvalov NS, 1989, Homogenisation: averaging processes in periodic media: mathematical problems in the mechanics of composite materials, DOI [10.1007/978-94-009-2247-1, DOI 10.1007/978-94-009-2247-1]

[6]

Borisov DI, 2003, ASYMPTOTIC ANAL, V35, P1

[7] On boundary-value problems for the Laplacian in bounded domains with micro inhomogeneous structure of the boundaries [J].

Chechkin, Gregory A. ;

Gadyl'Shin, Rustem R. .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2007, 23 (02) :237-248

[8]

Cioranescu D., 2016, PORT MATH, V63, P467

[9] ASYMPTOTIC-EXPANSION FOR A PERIODIC BOUNDARY-CONDITION [J].

FILO, J ;

LUCKHAUS, S .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 120 (01) :133-173

[10]

FILO J., 1998, ARCH MATH, V34, P83

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