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(An Iteration Method for the Riemann Problem of Some Degenerate Hyperbolic Balance Laws)

 ★ 氣流的非黏性駐波通過不連續管子之探究 ★ 影像模糊方法在蝴蝶辨識神經網路中之應用 ★ 單一非線性平衡律黎曼問題廣義解的存在性 ★ 非線性二階常微方程組兩點邊界值問題之解的存在性與唯一性 ★ 對接近音速流量可壓縮尤拉方程式的柯西問題去架構區間逼近解 ★ 一些退化擬線性波動方程的解的性質. ★ 擬線性波方程中片段線性初始值問題的整體Lipchitz連續解的 ★ 水文地質學的平衡模型之擴散對流反應方程 ★ 非線性守恆律的擾動Riemann 問題的古典解 ★ BBM與KdV方程初始邊界問題解的週期性 ★ 共振守恆律的擾動黎曼問題的古典解 ★ 可壓縮流中微黏性尤拉方程激波解的行為 ★ 非齊次雙曲守恆律系統初始邊界值問題之整域弱解的存在性 ★ 有關非線性平衡定律之柯西問題的廣域弱解 ★ 單一雙曲守恆律的柯西問題熵解整體存在性的一些引理 ★ 二階非線性守恆律的整體經典解

★ degenerate hyperbolic balance laws
★ shcok waves
★ rarefaction waves
★ Riemann problem

Contents………………………………………………………………………………………………………iii
Abstract………………………………………………………………………………………………………1
1. Introduction………………………………………………………………………………………………1
2. Solution of Generalized Riemann Problem (1.5) …………………………………………………………3
3.………………………………………………………………………………………………………………6
4. Using the method of characteristic to find solutions of two Riemann problems…………………………8
References……………………………………………………………………………………………………12

systems 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 Comprehensive
Studies 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, De nition 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. Pure
Appl. Math. 18 (1956), pp. 697-715.
[7] J. Groah, J. Smoller, B. Temple, Shock Wave Interactions in General Relativity, Monographs
in Mathematics, Springer, Berlin, New York, 2007.
[8] J.M. Hong, An extension of Glimm’s method to inhomogeneous strictly hyperbolic systems
of 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 solutions
of 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 trac
ow, to appear in Trans-
portation research, Part B.
[14] B. Key tz, H. Kranzer, A system of non-strictly hyperbolic conservation laws arising in
elasticity 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 nonconservative
form, 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 di erent 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-Di usion 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 large
time-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 hyperbolic
conservation laws, Adv. Appl. Math., 3 (1982), pp. 335-375.
[27] B. Whitham, Linear and nonlinear waves, New York : John Wiley, 1974.