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研究生:張嘉宏
研究生(外文):Chia-Hung Chang
論文名稱(外文):An Iteration Method for the Riemann Problem of Some Degenerate Hyperbolic Balance Laws
指導教授:洪盟凱洪盟凱引用關係
學位類別:碩士
校院名稱:國立中央大學
系所名稱:數學系
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:2013
畢業學年度:101
語文別:英文
論文頁數:20
中文關鍵詞:黎曼問題
外文關鍵詞:Hyperbolic systems of conservation lawsdegenerate hyperbolic balance lawsshcok wavesrarefaction wavesRiemann problem
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於此篇文章中我們考慮的是一個2 × 2退化的雙曲型守恆律系統,而我們考慮的這一個系統它的第二行方程式缺乏了對時間微分的項。本篇文章主要是研究這個系統的黎曼問題。我們將介紹一種疊代方式去建構這個系統的弱解。其中這些弱解的建構過程中是依據特徵線方法、Rankine-Hugonniot 條件以及分析上疊代方式而獲得。
In this thesis, we consider a 2 × 2 degenerate hyperbolic system of conservation laws whose second equation does not have the term related to the time-derivative of unknowns. The Riemann problem of such conservation laws is studied. We introduce an iteration scheme to construct the weak solutions of the Riemann problem. The weak solutions are obtained based on the characteristic method, Rankine-Hugoniot condition for discontinuous solutions and the iteration to the elementary waves for homogeneous systems.
中文摘要………………………………………………………………………………………………………i
英文摘要………………………………………………………………………………………………………ii
Contents………………………………………………………………………………………………………iii
Abstract………………………………………………………………………………………………………1
1. Introduction………………………………………………………………………………………………1
2. Solution of Generalized Riemann Problem (1.5) …………………………………………………………3
3.………………………………………………………………………………………………………………6
4. Using the method of characteristic to find solutions of two Riemann problems…………………………8
References……………………………………………………………………………………………………12
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