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研究生： 林逸凱
Lin, Yi-Kai
論文名稱： 探討具有邊界效應的一維黏性守恆定律的震波傳遞
A literature review of shock propagation for one dimensional viscous conservation laws with boundary effect
指導教授： 郭鴻文
Kuo, Hung-Wen
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年： 2022
畢業學年度： 110
語文別： 英文
論文頁數： 31
中文關鍵詞： 邊界效應 、格林函數 、守恆律 、黏滯型震波
外文關鍵詞： boundary effect, Green's function, conservation law, viscous shock profile
相關次數： 點閱：102  下載：23 
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    • 在本論文中，我們透過考慮具有黏滯性的 Burgers 方程來探討具有邊界效應的震波
    傳遞。我們論述[5]的證明並詳細說明他的概念。此外，我們應用拉普拉斯變換及複
    分析求解帶有 Robin 邊界條件的熱方程。

    In this paper, we review the viscous shock propagation with boundary effect by con-
    sidering the Burgers equation. We go through the proofs in [5] and elaborate on its
    conception. In addition, we solve a heat equation with Robin boundary condition based on the Laplace transform and complex analysis.

    1 Introduction 1 2 Outlines of the Theorems and Lemmas 9 3 Framework of our analysis and calculation 12 3.1 Estimates of α and α′ 12 3.2 Proof of Lemma 4 14 3.3 Sketch of the proof of Theorem 5 20 3.4 Sketch of the proof of Theorem 8 24 3.5 Sketch of the proof of Lemma 10 27 3.6 Sketch of the proof of Theorem 1 28 3.7 Sketch of the proof of Theorem 2 29 References 31

    [1] KT Joseph. Burger’s equation in the quarter plane, a formula for the weak limit.
    Communications on pure and applied mathematics, 41(2):133–149, 1988.
    [2] Chiu-Ya Lan, Huey-Er Lin, Tai-Ping Liu, and Shih-Hsien Yu. Propagation of vis-
    cous shock waves away from the boundary. SIAM journal on mathematical analysis,
    36(2):580–617, 2004.
    [3] Tai-Ping Liu and Kenji Nishihara. Asymptotic behavior for scalar viscous conser-
    vation laws with boundary effect. Journal of differential equations, 133(2):296–320,
    1997.
    [4] Tai-Ping Liu and Shih-Hsien Yu. Propagation of a stationary shock layer in the
    presence of a boundary. Archive for Rational Mechanics and Analysis, 139(1):57–82,
    1997.
    [5] LC Tsai. Viscous shock propagation with boundary effect. Bull. Inst. Math. Acad.
    Sin.(NS), 6:1–25, 2011.

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