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姓名	呂佳孃(Chia-niang Lu)  查詢紙本館藏	畢業系所	數學系
論文名稱	Regularized Buckley-Leverett方程的行進波解 (Traveling Wave Solutions to theRegularized Buckley-Leverett Equation)
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摘要(中)	在本文中，主要研究Regularized Buckley-Leverett 方程行進波解的存在性，這個問題可以簡化成兩點邊界值問題的微分方程。在給定邊界條件下，使得這個邊界值問題可以有三個平衡點。在特殊的邊界條件下，行進波解的存在性是可以在Poincare-Bendixson 定理和在Stable Manifold定理下的trapping region method證明出來。
摘要(英)	In this thesis, we study the existence of traveling wave solutions to the regularized　Buckley-Leverett equation. The problem can be reduced to a two point boundary value problem of some ordinary differential equation. We give the conditions of boundary data such that the two point boundary value problem has exactly three equilibria. The existence of traveling wave solutions for some special boundary data are provided by Poincar´e-Bendixson Theorem, and trapping region method for Stable Manifold Theorem.
關鍵字(中)	★ 守恆定律 ★ 兩點邊界值問題 ★ Poincar´e-Bendixson 定理 ★ Stable Manifold 定理 ★ Regularized Buckley-Leverett 方程 ★ 行進波 ★ dispersive方程	關鍵字(英)	★ Stable Manifold Theorem ★ traveling waves ★ conservation laws ★ dispersive equations ★ Regularized Buckley-Leverett equation ★ Poincar´e-Bendixson Theorem ★ two point boundary value problem
論文目次	中文摘要………………………………………………………………i 英文摘要…………………………………………………………… ii Contents……………………………………………………………iii 1. Introduction……………………………………………………01 2. Derivation of Regularized Buckley-Leverett Equation…02 3. Equilibria of Equation for Traveling Waves……………05 4. Existence of Traveling Wave Solutions…………………10 5. References……………………………………………………21
參考文獻	[1] C. J. Van Duijn, A. Mikelic, and I. S. Pop. Effective equations for two-phase flow with trapping on the micro scale. SIAM Journal on Applied Mathematics, 62(5):1531V1568, 2002. [2] S. Hassanizadeh and W. Gray. Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv. Water Resour., 13:169V186, 1990. [3] S. Hassanizadeh andW. Gray. Thermodynamic basis of capillary pressure in porous media. Water Resour. Res., 29:3389V3405, 1993. [4] A. Corey. The interrelation between gas and oil relative permeabilities. Producers Monthly, 19(1):38V41, 1954. [5] C. J. Van Duijn, A. Mikelic, and I. Pop. Effective Buckley-Leverett equations by homogenization. Progress in industrialmathematics at ECMI, pages 42V52, 2000. [6] D. Aronson and H. Weinberg : Nonlinear diffusion in population genetics,combustion, and nerve conduction,in Partial Differential Equations and Related Topics, ed ,J. A. Goldstein, Lecture Note in Mathematics 446, 5-49,New York: Springer, (1975) [7] P. C. Fife and J. B. McLeod : The Approach of Solutions of Nonlinear Diffusion Equations to Travelling Front Solutions, Archiv. Rat. Mech. Anal.65,335-361 (1977). [8] J. Glimm,Solutions in the large for nonlinear hyperbolic systems of equations,Comm. Pure Appl. Math. 18(1956) 697-715. [9] J. Hong, B. Temple, The generic solution of the Riemann problem in a neighborhood of a point of resonance for sysytems of nonlinear balance laws,Methods Appl. Anal. 10 (2) (2003) 279-294. [10] J. 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. 64 (3) (2004) 819-857 [11] P.D. Lax, Hyperbolic system of conservation laws, II, Comm. Pure Appl.Math. 10 (1957) 537-566.22 [12] T.P.Liu, Quasilinear hyperbolic sysytems, Comm. Math. Phys. 68 (1979)141-172. [13] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer,Berlin, New York, 1983. [14] B. Temple, Global solution of the Cauchy problem for a calss of 2x2 nonstrictly hyperbolic conservation laws,Adv. Appl. Math. 3 (1982) 335-375 [15] S.N. Kruzkov, First order quasilinear equations with several space variables,Mat. USSR Sb. 10 (1970) 217-243 [16] P.D. Lax, Hyperbolic sysytem of conservation laws and mathematival theory of shock waves, Conference Board ofMathematical Sciences, vol. 11,SIAM, Philadelpia, PA, 1973. [17] O.A. Oleinik, Discontinous solutions of non-linear different equations, Uspekhi Math. Nauk.(N.S.) 12 (1957) 3-73 (Transactions of the American Mathematical Society Series 2, vol. 26, pp. 172-195). [18] B. Whitham, Linear and Nonlinear Waves, Wiley, New York, 1974. [19] Y.Wang, Central schemes for the modified Buckley-Leverett equation, Ph.D.thesis, Ohio State Univ., 2010.
指導教授	洪盟凱(John M. Hong)	審核日期	2011-7-6
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