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研究生： 姚文銘
Man-meng Io
論文名稱： 共振守恆律的擾動黎曼問題的古典解
Classical Solutions to the Perturbed Riemann Problem of Scalar Resonant Balance Law
指導教授： 洪盟凱
John M. Hong
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
畢業學年度： 96
語文別： 英文
論文頁數： 24
中文關鍵詞： 擾動黎曼問題 、黎曼問題 、非線性平衡律 、特徵線法 、Lax''s 方法 、守恆律
外文關鍵詞： Perturbed Riemann problems, Riemann problems, Nonlinear balance laws, Conservation laws, Lax''s method, Characteristic method
相關次數： 點閱：9  下載：0 
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    • 在這篇論文中，我們探討單一非線性平衡律的擾動黎曼問題的古典解。此平衡律等價於一個二乘二非線性平衡系統，而且是一個共振的系統。
    透過特徵線的方法，我們建立擾動黎曼問題的古典解。經由此古典解的點態極限，我們並獲得對應之黎曼問題的解的自相似性。

    In this paper we study the classical solutions to the perturbed Riemann problem of some scalar nonlinear balance law in resonant case. The equation with source term is equivalent to a 2×2 nonlinear balance laws as described in [6, 7], and it is a resonant system due to the fact that the speeds of waves in the solution to this 2×2 system coincide. The characteristic method in [8] is applied to construct the classical solutions of perturbed Riemann problem. Moreover, we show that, the pointwise limit of classical solutions, which are defined as the
    measurable solutions to the corresponding Riemann problem (with singular source) of perturbed Riemann problem, are self-similar as described in [12].

    中文摘要 ………………………………………………………………i 英文摘要 ………………………………………………………………ii Acknowledgement ………………………………………………………iii 目錄 ……………………………………………………………………iv 圖目錄 …………………………………………………………………v 表目錄 ……………………………………………………………………vi 1. Introduction …………………………………………………………2 2. Classical solutions of perturbed Riemann problem …………5 3. Stability of perturbed Riemann solutions …………………17 References ………………………………………………………………23

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