Homogenization of the Boundary Value Problem for the Laplace Operator in a Domain Perforated along (n-1)-Dimensional Manifold with Nonlinear Robin Type Boundary Condition on the Boundary of Arbitrary Shaped Holes: Critical Case

被引：2

作者：

Podolskiy, A. V. ^{[1
]}

Shaposhnikova, T. A. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow 119992, Russia

来源：

DOKLADY MATHEMATICS | 2017年 / 96卷 / 03期

关键词：

D O I：

10.1134/S1064562417060229

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The asymptotic behavior of the solution to the boundary value problem for the Laplace operator in a domain perforated along an (n - 1)-dimensional manifold is studied. A nonlinear Robin-type condition is assumed to hold on the boundary of the holes. The basic difference of this work from previous ones concerning this subject is that the domain is perforated not by balls, but rather by sets of arbitrary shape (more precisely, by sets diffeomorphic to the ball). A homogenized model is constructed, and the solutions of the original problem are proved to converge to the solution of the homogenized one.

引用

页码：601 / 606

页数：6

共 40 条

[1] Homogenization of the boundary value problem for the Laplace operator in a domain perforated along (n – 1)-dimensional manifold with nonlinear Robin type boundary condition on the boundary of arbitrary shaped holes: Critical case
A. V. Podolskiy
T. A. Shaposhnikova
[J]. Doklady Mathematics, 2017, 96 : 601 - 606
[2] Homogenization of the boundary value problem for the laplace operator in a perforated domain with a rapidly oscillating nonhomogeneous Robin-type condition on the boundary of holes in the critical case
M. N. Zubova
T. A. Shaposhnikova
[J]. Doklady Mathematics, 2017, 96 : 344 - 347
[3] Homogenization of the boundary value problem for the laplace operator in a perforated domain with a rapidly oscillating nonhomogeneous Robin-type condition on the boundary of holes in the critical case
Zubova, M. N.
Shaposhnikova, T. A.
[J]. DOKLADY MATHEMATICS, 2017, 96 (01) : 344 - 347
[4] Homogenization limit for the boundary value problem with the P-laplace operator and a nonlinear third boundary condition on the boundary of the holes in a perforated domain
A. V. Podol’skii
[J]. Doklady Mathematics, 2010, 82 : 942 - 945
[5] Homogenization Limit for the Boundary Value Problem with the P-Laplace Operator and a Nonlinear Third Boundary Condition on the Boundary of the Holes in a Perforated Domain
Podol'skii, A. V.
[J]. DOKLADY MATHEMATICS, 2010, 82 (03) : 942 - 945
[6] Averaging of boundary-value problem in domain perforated along (n-1)-dimensional manifold with nonlinear third type boundary conditions on the boundary of cavities
Lobo, M.
Perez, M. E.
Sukharev, V. V.
Shaposhnikova, T. A.
[J]. DOKLADY MATHEMATICS, 2011, 83 (01) : 34 - 38
[7] Homogenization for the p-Laplace operator and nonlinear Robin boundary conditions in perforated media along (n-1)-dimensional manifolds
Gomez, D.
Lobo, M.
Perez, E.
Podolskiy, A. V.
Shaposhnikova, T. A.
[J]. DOKLADY MATHEMATICS, 2014, 89 (01) : 11 - 15
[8] Homogenization of a Boundary Value Problem for the n-Laplace Operator on a n-Dimensional Domain with Rapidly Alternating Boundary Condition Type: The Critical Case
A. V. Podolskiy
T. A. Shaposhnikova
[J]. Differential Equations, 2019, 55 : 523 - 531
[9] Homogenization of a Boundary Value Problem for the n-Laplace Operator on a n-Dimensional Domain with Rapidly Alternating Boundary Condition Type: The Critical Case
Podolskiy, A. V.
Shaposhnikova, T. A.
[J]. DIFFERENTIAL EQUATIONS, 2019, 55 (04) : 523 - 531
[10] Homogenization limit for the initial-boundary value problem for a parabolic equation with p-laplace operator and a nonlinear third boundary condition on the boundary of the holes in a perforated domain
A. V. Podol’ski
[J]. Doklady Mathematics, 2012, 86 : 791 - 795

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