| On Boundary-Value Problems for the Laplacian in Bounded Domains with Micro Inhomogeneous Structure of the Boundaries |
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| 引用本文： | Gregory A. CHECHKIN Rustem R. GADYL＇SHIN. On Boundary-Value Problems for the Laplacian in Bounded Domains with Micro Inhomogeneous Structure of the Boundaries[J]. 数学学报(英文版), 2007, 23(2): 237-248. DOI: 10.1007/s10114-005-0849-1 |
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| 作者姓名： | Gregory A. CHECHKIN Rustem R. GADYL＇SHIN |
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| 作者单位： | [1]Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow State University, Moscow 119992, Russia [2]Narvik University College, 8505 Narvik, Norway [3]Institute of Mathematics with Computing Center, Russian Academy of Sciences, Ufa 450077, Russia [4]Department of Mathematical Analysis, Faculty of Physics and Mathematics, Bashkir State Pedagogical University, Ufa 450000, Russia |
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| 基金项目： | The research is partially supported by the program ＂Leading Scientific Schools＂ and by RFBR,Acknowledgments The paper was completed in Narvik University College （HiN） in Northern Norway during the cold January 2003. The authors express thanks to the authority of Narvik University College for the wonderful work conditions and for their support. |
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| 摘 要： | We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type.
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| 关 键 词： | 边界条件 边值问题 微非均质结构 拉普拉斯算子 均匀化 |
| 修稿时间： | 2003-12-022006-01-10 |
On Boundary-Value Problems for the Laplacian in Bounded Domains with Micro Inhomogeneous Structure of the Boundaries |
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| Gregory A. Chechkin,Rustem R. Gadyl’shin. On Boundary-Value Problems for the Laplacian in Bounded Domains with Micro Inhomogeneous Structure of the Boundaries[J]. Acta Mathematica Sinica(English Series), 2007, 23(2): 237-248. DOI: 10.1007/s10114-005-0849-1 |
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| Authors: | Gregory A. Chechkin Rustem R. Gadyl’shin |
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| Affiliation: | (1) Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow State University, Moscow 119992, Russia;(2) Narvik University College, 8505 Narvik, Norway;(3) Institute of Mathematics with Computing Center, Russian Academy of Sciences, Ufa 450077, Russia;(4) Department of Mathematical Analysis, Faculty of Physics and Mathematics, Bashkir State Pedagogical University, Ufa 450000, Russia |
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| Abstract: | In this paper, we consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized (limit) problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type. The research is partially supported by the program “Leading Scientific Schools” and by RFBR |
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| Keywords: | homogenization rapidly alternating boundary conditions spectral problems |
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