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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………………………………………………………………………………………………………iiContents………………………………………………………………………………………………………iiiAbstract………………………………………………………………………………………………………11. Introduction………………………………………………………………………………………………12. Solution of Generalized Riemann Problem (1.5) …………………………………………………………33.………………………………………………………………………………………………………………64. Using the method of characteristic to find solutions of two Riemann problems…………………………8References……………………………………………………………………………………………………12
 [1] D. Amadori, L. Gosse, G. Guerra, Global BV entropy solutions and uniqueness for hyperbolicsystems of balance laws, Arch. Rational Mech. Anal. 162 (2002) pp. 327-366.[2] Y. Chang, J.M. Hong, C.-H. Hsu, Globally Lipschitz continuous solutions to a class of quasi-linear wave equations, J. Di. Equ. 236 (2007), pp. 504-531.[3] C.M. Dafermos, Hyperbolic conservation laws in continuum physics, Series of ComprehensiveStudies in Mathematics, Vol. 325, Springer.[4] C.M. Dafermos, L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dis-sipation, Indiana U. Math. J. 31 (1982), pp. 471-491.[5] G. Dal Maso, P. LeFloch, F. Murat, Denition and Weak Stability of Nonconservative Prod-ucts, J. Math. Pures Appl. 74 (1995), pp. 483-548.[6] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. PureAppl. Math. 18 (1956), pp. 697-715.[7] J. Groah, J. Smoller, B. Temple, Shock Wave Interactions in General Relativity, Monographsin Mathematics, Springer, Berlin, New York, 2007.[8] J.M. Hong, An extension of Glimm's method to inhomogeneous strictly hyperbolic systemsof conservation laws by \weaker than weak" solutions of the Riemann problem, J. Di. Equ.222 (2006), pp. 515-549.[9] J.M. Hong, C.H. Hsu, Y.-C. Su, Global solutions for initial-boundary value problem of quasi-linear wave equations, J. Di. Equ. 245 (2008), pp. 223-248.[10] J.M. Hong, P.G. LeFloch, A version of Glimm method based on generalized Riemann prob-lems, J. Portugal Math., Vol. 64, (2007) pp. 199-236.[11] J.M. Hong, B. Temple, A bound on the total variation of the conserved quantities for solutionsof a general resonant nonlinear balance law, SIAM J. Appl. Math., Vol. 64, No. 3 (2004) pp.819-857.[12] E. Isaacson, B. Temple, Nonlinear resonant in inhomogenous systems of conservation laws,Cotemp. Math., 108, 1990.[13] Wen-Long Jin, A kinematic wave theory of lane-changing tracow, to appear in Trans-portation research, Part B.[14] B. Keytz, H. Kranzer, A system of non-strictly hyperbolic conservation laws arising inelasticity theory, Arch. Ration. Mech. Anal., 72 (1980), pp. 219-241.[15] S.N. Kruzkov, First order quasilinear equations with several space variables, Mat. USSR Sb.,10 (1970), pp. 217-243.[16] P.D. Lax, Hyperbolic system of conservation laws, II, Comm. Pure Appl. Math., 10 (1957),pp. 537-566.[17] P.D. Lax, Hyperbolic system of conservation laws and mathematical theory of shock waves.,Conf. Board Math. Sci., 11, SIAM, 1973.[18] P.G. LeFloch, Entropy Weak Solutions to Nonlinear Hyperbolic Systems Under Nonconser-vative Form, Comm. Part. Di. Eq., 13 (1988), pp 669-727.[19] P.G. LeFloch, T.P. Liu, Existence theory for nonlinear hyperbolic systems in nonconservativeform, Forum Math. 5 (1993), pp. 261-280.[20] T.P. Liu, Quasilinear hyperbolic systems, Comm. Math. Phys., 68 (1979), pp. 141-172.[21] M. Luskin and B. Temple, The existence of a global weak solution to the non-linear water-hammer problem, Comm. Pure Appl. Math. 35 (1982), pp. 697-735.[22] T. Nishida, J. Smoller, Mixed problems for nonlinear conservation laws, J. Di. Equ. 23(1977), pp. 244-269.[23] O.A. Oleinik, Discontinuous solutions of non-linear dierent equations, Uspekhi Math.Nauk(N.S.), 12 (1957), pp. 3-73. (Trans. Amer. Math. Soc., Ser. 2, 26, pp. 172-195.)[24] J. Smoller, Shock Waves and Reaction-Diusion Equations, 2nd ed., Springer-Verlag, Berlin,New York, 1994.[25] Ying-Chin Su, Global entropy solutions to a class of quasi-linear wave equations with largetime-oscillating sources , J. Di. Equ. Issue 9 Volume 250, (2011), pp. 3668-3700.[26] B. Temple, Global solution of the Cauchy problem for a class of 2 2 nonstrictly hyperbolicconservation laws, Adv. Appl. Math., 3 (1982), pp. 335-375.[27] B. Whitham, Linear and nonlinear waves, New York : John Wiley, 1974.
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 1 一些退化擬線性波動方程的解的性質.

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 1 無線網格網路之多路徑路由分析與設計 2 Numerical Computation of Riemann Problem for a Degenerate Hyperbolic System of Conservation Laws 3 探討台灣加權指數、信用交易、外資買賣與匯率關聯性 4 拉伸流場中紅血球破壞探討 5 Vector Fields With Given Vorticity, Divergence And The Normal Trace 6 Two-Level Deflated Preconditioners for Sparse Symmetric Positive Define Linear Systems with Approximate Eigenvector Approach 7 針對智慧型手機之健康照護應用程式進行可靠性及適用性之評估 8 以投影Lanczos法解三維光子晶體的特徵值問題 9 Mathematical Modeling and Numerical Simulation for Transport Phenomena in Porous Medium 10 Nonlinear Balance Laws with Rotational Source Terms 11 Nonlinear Hyperbolic Systems of Conservation Laws in Symmetric Space-Application to Shallow Water Equations 12 線上問卷調查開發應用與Matlab對於微積分學習成效之探討 13 Nonlinear Balance Laws in Traffic Flow – A Model with Lane-changing Intensity 14 VMO Associated to the Sections 15 Conformality of Planar Parameterization for Single Boundary Triangulated Surface Mesh

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