透過您的圖書館登入
IP:216.73.216.156
  • 學位論文

一些特殊退化二次橢圓算子的勻質化問題與計算

Homogenization of some special degenerate second order linear elliptic operators and its numerical computation

指導教授 : 朱家杰

摘要


我們在這篇論文中討論了一些特殊退化二次橢圓算子的勻質化問題, 並利用有限元素法做了幾個數值上的計算

並列摘要


Abstract Homogenization of some special degenerate second order linear elliptic operators and its numerical computation Lin-Hong Shen, Avisor:Assistant Professor Chia-Chieh Chu Department of Mathematics National Tsing Hua University, Hsin-Chu City,Taiwan In many area, homogenization is an alternative way to find out the asymptotic behaviour of partial differential equation. This arti- cle is about homogenization process of degenerate second order linear elliptic operators. In this article, we give both theoretical and com- putational analysis to the asymptotic behaviour of the solution of the equation. −div(a( x )Duh) = f on Ω , uh |∂Ω= 0 on ∂Ω , when Eh tends to zero, where aij (x) is Y -periodic, nonnegative defi- nite for almost every x in domain Ω and vanishes at some points in Ω. We find out that the homogenization process of degenerate ellip- tic equation in rectangle domain is still available for some particular coefficient functions with its inverse is integrable Key words: homogenization, degenerate elliptic equation, asymp- totic behaviour, numerical analysis

參考文獻


[BS08] Susanne C. Brenner and L.Ridgway Scott. The mathematical theory of the finite element methods. Springer, 2008.
[Cav02] Albo Carlos Cavalheiro. An approximation theorem for solutions of degenerate elliptic equations. Proc. Edinb. Math. Soc. (2), 45:363– 389, 2002.
[Def93] Anneliese. Defranceschi. An introduction to homogenization and g-convergence. Technical report, ICTP, September 1993.
[FKS82] E. Fabes, C. Kenig, and R. Serapioni. The local regularity of so- lutions of degenerate elliptic equations. Communication in PDEs, 7(1):77–116, 1982.
[GT77] D. Gilbarg and N. Trudinger. Elliptic partial differential equations of second order. Springer-Verlag, Berlin, 1977.

延伸閱讀