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研究生:李昱霆
研究生(外文):Yu-ting Lee
論文名稱(外文):Nonlinear Balance Laws in Traffic Flow – A Model with Lane-changing Intensity
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:19
中文關鍵詞:守恆定律
外文關鍵詞:Balance lawLane-changing intensity
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於此篇文章中我們主要探討並研究一個關於交通流的非線性雙曲型守恆定律。此交通流的模型包含著一個能夠表示車道變換之車輛的強度的參數。這模型可以重寫成一個含有源項的守恆定律的形式(亦即此守恆定律方程式之等號右側帶有非零項)。此文章亦會展示幾種不同案例的車道變換強度之數值計算結果。
In this thesis we study a nonlinear hyperbolic balance law arise from traffic flow. The model of traffic flow consists of a parameter representing the intensity of lane-changing of vehicles. The model is rewritten as a balance law with source terms. The numerical results are given for different cases of lane-changing intensities.
中文摘要 ……………………………………………………… i
英文摘要 ……………………………………………………… ii
目錄 ……………………………………………………… iii
論文本文 ……………………………………………………… 1
1. Introduction……………………………………… 2
2. Model of lane-changing traffic flow………… 5
3. Finite difference method………………………. 7
4. Numerical solutions……………………………. 11
Reference ……………………………………………………… 17

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[4] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18(1965), pp. 697-715.
[5] S.K. Godunov, A difference method for numerical calculations of discontinu- ous solutions of the equations of hydrodynamics, Mat. Sb. 47(1959), in Rus- sion, pp. 271-306.
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[7] E. Isaacson, Global solution of a Riemann problem for a non-strictly hyper- bolic system of conservation laws arising in enhanced oil recovery, Rockefeller University preprint.
[8] E. Isaacson, D. Marchesin, B. Plohr, and B. Temple The Riemann problem near a hyperbolic singularity: the classification of solutions of quadratic Rie- mann problems I, SIAM J. Appl. Math.,48(1988), pp. 1009-1052.
[9] E. Isaacson, B. Temple, The structure of asymptotic states in a singular sys- tem of conservation laws, Adv. Appl. Math., 11(1990), pp. 205-219.
[10] E. Isaacson, B. Temple, Analysis of a singular hyperbolic system of conserva- tion laws, Jour. Diff. Equn., 65(1986), pp. 250-268.
[11] E. Isaacson, B. Temple, Examples and classification of non-strictly hyperbolic systems of conservation laws, Abstracts of AMS, January 1985. 
50
[12] E. Isaacson, B. Temple, Nonlinear resonance in systems of conservation laws, with E. Isaacson, SIAM Jour. Appl. Anal., 52, 1992, pp. 1260-1278.
[13] E. Isaacson, B. Temple, Convergence of the 2 × 2 Godunov method for a general resonant nonlinear balance law, SIAM Jour. Appl. Math., 55, No. 3, pp. 625-640, June 1995.
[14] B. Keyfitz and H. Kranzer, A system of non-strictly hyperbolic conservation laws arising in elasticity theory, Arch. Rat. Mech. Anal., 72(1980), pp.219- 241.
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[18] L. Lin, J. Wang and B. Temple, A comparison of convergence rates for Go- dunov’s method and Glimm’s method in resonant nonlinear systems of con- servation laws, with L.Lin and J. Wang., SIAM J. Numer. Anal., 32, No. 3, pp. 824-840.
[19] L. Lin, J. Wang and B. Temple, Suppression of oscillations in Godunov’s method for a resonant non-strictly hyperbolic system, SIAM J. Numer. Anal., 32, No. 3, June 1995.
[20] T.P. Liu, Quasilinear hyperbolic systems, Comm. Math. Phys., 68(1979), pp. 141-172.
[21] T.P. Liu, Resonance for a quasilinear hyperbolic equation, J. Math. Phys. 28 (11), (1987), pp. 2593-2602.
[22] D. Marchesin and P.J. Paes-Leme, A Riemann problem in gas dynamics with bifurcation, PUC Report MAT 02/84, 1984.
[23] O.A. Oleinik, Discontinuous solutions of non-linear differential equations, Us- pekhi Mat. Nauk (N.S.), 12(1957),no.3(75), pp. 3-73 (Am. Math. Soc. Trans., Ser. 2, 26, pp. 195-172.)
[24] J. Smoller, Shock waves and reaction diffusion equations, Springer-Verlag, Berlin, New York, 1983. 
51
[25] B. Temple, Global solution of the Cauchy problem for a class of 2 × 2 non- strictly hyperbolic conservation laws, Adv. in Appl. Math., 3(1982), pp. 335- 375.
[26] A. Tveito and R. Winther, Existence, uniqueness and continuous depen- dence for a system of hyperbolic conservation laws modelling polymer flooding, Preprint, Department of Informatics, University of Oslo, Norway, January, 1990.
[27] Wen-Long Jin *, A kinematic wave theory of lane-changing traffic flow, November 25, 2009.
[28] Wen-Long Jin *, A multi-commodity Lighthill-Whitham-Richards model of lane-changing traffic flow, Department of Civil and Environmental Engineering, University of California, 2012.

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