Recent Progress in the Theory of the Dam Problem
Bibliographic Information
- Other Title
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- ダム問題に対する最近の進展
- ダム モンダイ ニ タイスル サイキン ノ シンテン
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Abstract
In this paper, we present a scheme of convergence analysis of trial free boundary methods for the two-dimensional filtration (or dam) problem. For the purpose we present a new variational principle of the filtration problem. This variational principle is defined on the set of admissible domains (candidates of the solution) in the dam. Under mild assumptions on the configuration of the dam, we may assume that all admissible domains are mapped from the unit disk by conformal mappings. Thus, proving convergence of trial free boundaries is reduced to proving convergence of the conformal mappings on the unit disk, and it is done using a method in the theory of minimal surfaces.
Journal
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- Bulletin of the Japan Society for Industrial and Applied Mathematics
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Bulletin of the Japan Society for Industrial and Applied Mathematics 15 (1), 16-31, 2005
The Japan Society for Industrial and Applied Mathematics
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Details 詳細情報について
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- CRID
- 1390001205766828800
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- NII Article ID
- 110001888933
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- NII Book ID
- AN10288886
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- ISSN
- 09172270
- 24321982
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- NDL BIB ID
- 7297213
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- CiNii Articles
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- Abstract License Flag
- Disallowed
