Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/29676


Title: 一些非線性方程解的存在性
Existence of solutions for some nonlinear equations
Authors: 陳品均
Contributors: 李明融
陳品均
Keywords: 震波
稀疏波
Date: 2008
Issue Date: 2009-09-11 16:02:00 (UTC+8)
Abstract: 在這篇文章中,我們討論守恆方程∂_{t}u+∂_{x}f(u)=0解的存在性。我們藉由觀察物理現象和實驗結果討論這樣的問題。我們利用特徵曲線法並提出物理上的尺度分析法來找出某些非線性的方程式的解;特別針對通量函數為f(u)=u^2,u^3,-u^2,-u^3時,我們也發現守恆方程式的特別解。在某些實際上的意義下,我們將定義並找出震波集合和稀疏波集合,且找到了由有限個震波和稀疏波所組成的古典自相似解。
Reference: [1] Culbert B.L., Computational Gasdynamics, Cambridge University Press, 1998.
[2] LeFloch P.G., Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves, Birkhäuser Verlag, 2002.
[3] Teubner B.G., Numerical Schemes for Conservation Laws, John Wiley and Sons Ltd, 1997.
[4] Tzong-Hann Shieh, Meng-Rong Li, Numerical treatment of contact discontinuity with multi-gases, Journal of computational and applied mathematics, 2009 to appear.
[5] Tzong-Hann Shieh, Meng-Rong Li, Modeling and numerical treatment of contact discontinuity with difference gases, 2009, preprint.
Description: 碩士
國立政治大學
應用數學研究所
95751001
97
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0095751001
Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

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