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研究生:賴佳妤
研究生(外文):Chia-yu Lai
論文名稱(外文):Nonlinear Hyperbolic Systems of Conservation Laws in Symmetric Space-Application to Shallow Water Equations
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:30
中文關鍵詞:質量守恆律非線性雙曲系統對稱空間淺水波方程
外文關鍵詞:Conservation lawsNonlinear hyperbolic systemssymmetric Spaceshallow water equations
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在本論文中,在分析Shallow water equation 時,通常會先探討伴隨科氏力的三維Navier-Stokes Equation,接著會忽略垂直數度分布,將三維的Navier-Stokes Equation 推導成二維的Shallow water equation,並同乘以一個旋轉矩陣,使二維的Shallow water equation 消去source term。可在對稱空間中做座標轉換,進而使二維的Shallow water equation 成為一雙曲型系統的conservation laws。
In this paper , we consider the following three dimension shallow water equations with Coriolis force then we derived the two dimension shallow water equation . And we transformed the two dimension shallow water equation 3by3 conservative system without source term . We can use the results in traditional hyperbolic systems of conservation laws to study the shock waves and rarefaction waves.
1. Introduction.....................................1
2. Generalization to shallow water equations........4
3. Transformation of shallow water equations........7
3.1 The shallow water equations.....................7
3.2 Symmetric space.................................12
3.3 Traveling waves.................................18
4. The Rankine-Hugoniot condition...................22
Reference...........................................23
[1] C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, 2nd edition.
Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathemati-
cal Sciences], 325. Springer-Verlag, Berlin, 2005.
[2] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm.
Pure Appl. Math. 18 (1965), pp. 697-715.
[3] Jonathan Goodman, Zhouping Xin, Viscous Limits for Piecewise Smooth Solutions to
System of Conservation Laws, Arch. Rational Mech. Anal. 121 (1992), pp. 235-265.
[4] Benoit Cushman-Roisin,Jean-Marie Beckers, Introduction to Geophysical Fluid Dynamics,
(2007).
[5] J. M. Hong, C. H. Hsu, Y. C. Su, Global solutions for initial-boundary value problem of
quasilinear wave equations, J. Di. Equ. 245 (2008), pp. 223-248.
[6] P. D. Lax, Hyperbolic system of conservation laws, II, Comm. Pure Appl. Math. 10 (1957),
pp. 537-566.
[7] J. Smoller, Shock Waves and Reaction Diusion Equations, Springer-Verlag, New York,
Berlin (1983).
[8] B. Whitham, Linear and nonlinear waves. New York, John Wiley, 1974.
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