Averaging operators with boundary conditions of fine-scaled structure

被引：19
作者：
Belyaev, AY
Chechkin, GA
机构：
[1] Russian Acad Sci, Inst Water Problems, Moscow 117901, Russia
[2] Moscow MV Lomonosov State Univ, Moscow 117234, Russia
来源：
MATHEMATICAL NOTES | 1999年 / 65卷 / 3-4期
关键词：
function space; averaging problem; Laplace operator; Dirichlet and Neumann problem; rapidly oscillating boundary conditions; small parameter; fine scaled periodic structure; perforated domain of random structure;
D O I：
10.1007/BF02675355
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the averaging of boundary value problems with a small parameter in the boundary conditions. By using new notions, we prove the compactness theorem for at family of solutions. To verify the method proposed, we study a problem with rapidly varying boundary conditions in the case of a probabilistic description of the structure of the domain.
引用
收藏
页码：418 / 429
页数：12
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