簡易檢索 / 詳目顯示

回結果列表
研究生： 賀逸然
Yi-Jan Ho
論文名稱： T-C Scheme for the Linearized Equations of the Viscous Conservation Laws around a Viscous Shock Profile.
T-C Scheme for the Linearized Equations of the Viscous Conservation Laws around a Viscous Shock Profile.
指導教授： 林惠娥
Lin, Huey-Er
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 2014
畢業學年度： 102
語文別： 英文
論文頁數： 41
中文關鍵詞： T-C法 、守恆律 、黏滯型震波 、穿越波算子 、壓縮波算子
英文關鍵詞： T-C Scheme, Conservation Laws, Viscous Shock Profile, transversal wave operator, Compressive wave operator
論文種類： 學術論文
相關次數： 點閱：100  下載：15 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 在這篇論文中,我們假設函數Fi是黏滯型守恆律方程的一個解,且解的形式為黏滯型的震波。我們關心這樣的方程在Fi附近解的行為以及穩定性。這裡我們會介紹一個方法為T-C Scheme 它是用來建造對Fi線性化過後方程的解,並且對其解做估計來判斷原方程的穩定性,這篇文章只探討穿越波部分的估計。

    Assume Fi is a viscous shock profile of the viscous hyperbolic conservation laws. We are concerned with the stability and the solution structure for the initial value problem of the viscous hyperbolic conservation laws around the viscous shock wave Fi. The T-C scheme is used to estimate the solution of the linearized equations around viscous shock profile Fi. The detail proofs for the transversal wave operator of the T-C scheme are given in this thesis.

    1 Introduction… p2 2 The T-C scheme… p3 2.1 Green’s functions for the linearized equation around constant states . . . p3 2.2 T-C scheme operators . . . p5 2.2.1 Approximated solution operator. . . . p5 2.2.2 Error series operator and transversal wave operator. . . p6 2.2.3 Wave front operator. . . . p7 2.2.4 Compressive wave operator. . . . p8 2.2.5 T-C scheme . . . p9 3 Estimates on the transversal operator. p9 3.1 Main result . . . p9 3.2 Preparation for estimates. . . . p10 3.3 Error series operator. . . p12 3.4 Transversal wave operator. . . p20

    [1] Shijin Deng, WeikeWang, And Shih-Hsien Yu, Viscous conservation laws with boundary,
    SIAM J. Math. Anal., 44 (2012) no.4, pp. 2695-2755.
    [2] Shih-Hsien Yu, Nonlinear wave propagations over a Boltzmann shock pro.le, J. Amer.
    Math. Soc., 23(2010) no.4, pp. 1041-1118.
    [3] Tai-Ping Liu, Yanni Zeng, Large time behavior of solutions for general quasilinear
    hyperbolic-parabolic systems of conservation laws, Mem. Amer. Math. Soc., 125(1997)
    no.599.
    [4] Tai-Ping Liu, Nonlinear stability of shock waves for viscous conservation laws, Mem.
    Amer. Math. Soc., 56(1985).
    [5] Joel Smoller, Shock waves and reaction-di¤usion equations second edition, Springer-
    Verlag, 1994.
    [6] Lawrence C.Evans, Partial di¤erential equations, American Mathematical Society, 1998.
    [7] William E.Boyce, Richard C.Diprima, Elementary di¤erential equations and boundary
    value problems tenth edition, Wiley, 2013.
    [8] Fritz John, Partial di¤erential equations fourth edition, Springer-Verlag, 1982.

    下載圖示
    QR CODE