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研究生:陳侑萱
研究生(外文):You-Xuan Chen
論文名稱:在雙孔隙隨機介質上單相流的橢圓方程問題
論文名稱(外文):An elliptic problem for single phase flows in random media
指導教授:葉立明
指導教授(外文):Li-Ming Yeh
學位類別:碩士
校院名稱:國立交通大學
系所名稱:應用數學系所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:英文
論文頁數:13
中文關鍵詞:雙孔隙隨機介質單相流橢圓方程
外文關鍵詞:elliptic problemsingle phase flowsrandom media
相關次數:
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  • 下載下載:5
  • 收藏至我的研究室書目清單書目收藏:0
考慮一個通過兩種不同物質所組成、高度異質性多孔隨機介質上的線性單向流。我們以橢圓方程來描述此現象。藉由2-scale converge in the mean 的方法獲得均質化問題。
Consider the linearized equations of slightly compressible single fluid flows through a highly heterogeneous random porous medium, consisting of two types of material. Due to the high heterogeneity of the two materials, the ratio of their permeability coefficients is of order ε2, whereεis the characteristic scale of heterogeneities. A homogenized problem is obtained by using the stochastic two scale convergence in the mean and by means of convergence results adapted to a priori estimates and to the random geometry.
中文摘要 ………………………………………………………… i
英文摘要 ………………………………………………………… ii
誌謝 ………………………………………………………… iii
目錄 ………………………………………………………… iv
1. Introduction ……………………………………… 1
2. Ergodic dynamic system and relative theorems 1
3. ε-problem and main result ……………………… 4
4. A priori estimate…………………………………… 5
5. Stochastic two scale convergence…………………8
6. Auxiliary problem and convergence result………11
[1]A. Bourgeat, A. Mikelic and S.Wright, On the stochastic two-scale convergence in the mean and applications,J. Reine Angew. Math. (Crelles J.) 456 (1994),19-51.
[2] V.V. Jikov, S.M. Kozlov and O.A. Oleinik,Homogenization of Differential Operators and Integral Functionals, Springer, New York, 1994.
[3] A. Bourgeat, A. Mikelic and A. Piatnitski, On the double porosity model of single phase flow in random media, Asymptotic Analysis, 34 (2003), 311-332.
[4] E, Acerbi V, Chiado Piat, G. Dal Maso, and D. ercivale, An extension the-orem from connected sets, and homogenization in general periodic domains,Nonlinear Analysis 18(1992) 481-496
[5] Doina Cioranescu, Patrizia Donato, An Introduction to Homogenization, Oxford University Press, 1999.
[6] Lawrence C.Evans, Partial Dierential Equations, 1998.
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