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姓名 黃鵬翰(Peng-Han Huang)  查詢紙本館藏   畢業系所 數學系
論文名稱 單一雙曲守恆律的柯西問題熵解整體存在性的一些引理
(Some Lemmas for the Global Existence of Entropy Solutions to the Cauchy Problem of Single Dissipative Conservation Law)
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摘要(中) 在這篇論文中,我們考慮一個單一耗散雙曲守恆律。我們研究這種守恆律的初始值問題。我們使用原本由O. Oleinik提供的分析來建立這種初始值問題其熵解整體存在性。
摘要(英) In this thesis we consider a single dissipative hyperbolic scalar conservation law. We study
the initial value problem of such conservation law. We use the analysis originally provided
by O. Oleinik to establish the global existence of entropy solutions for such initial value
problem. In this thesis we will show some key lemmas to obtain the global existence
results.
關鍵字(中) ★ 雙曲守恆律
★ 初始值問題
★ 中央差分網格
★ 熵解
關鍵字(英) ★ central difference scheme
★ initial value problem
★ hyperbolic conservation laws
★ entropy solutions
論文目次 中文摘要............................................. i
英文摘要............................................. ii
目錄................................................. iii
圖目錄............................................... iv
Abstract............................................. 1
1 Introduction....................................... 2
2 The Proof of Lemmas................................ 4
References........................................... 11
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[2] C. Dafermos, Solutions of the Riemann problem for a class of conservation laws by the viscosity method, Arch. Ration. Mech. Anal., 52 (1973), pp. 1-9.
[3] C. Dafermos and L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dissipation, Indiana U. Math. Journal, 31, No. 4 (1982), pp. 471-491.
[4] G. Dal Maso, P. LeFloch and F. Murat, Definition and weak stability of nonconservative products, J. Math. Pure. Appl., 74 (1995), pp. 483-548.
[5] Ronald J. DiPerna, Measure-Valued Solutions to Conservation Laws, Arch. Ration. Mech. Anal., 88 , No. 3 (1985), pp. 223-270.
[6] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm.Pure Appl. Math., 18 (1965), pp. 697-715.
[7] 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. Diff. Equations, 222 (2006), pp. 515-549.
[8] J. M. Hong and 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, No 3 (2004), pp. 819-857
[9] J. M. Hong and P. G. LeFloch, A version of Glimm method based on generalized Riemann problem, Portugaliae Mathematica 64, Fasc. 2 (2007), pp. 199-236.
[10] E. Isaacson and B. Temple, Convergence of 2×2 by Godunov method for a general resonant nonlinear balance law, SIAM J. Appl. Math. 55 (1995), pp. 625-640.
[11] K. T. Joseph and P. G. LeFloch, Singular limits for the Riemann problem: general diffusion relaxation, and boundary condition, in ” new analytical approach to multidimensional balance laws”, O. Rozanova ed., Nova Press, 2004.
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[13] P. D. Lax, Hyperbolic system of conservation laws, II, Comm. Pure Appl. Math., 10 (1957), pp. 537-566.
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[18] O. A. Oleinik, Discontinuous solutions of nonlinear differential equations, Amer. Math. Soc. Transl. Ser. 2, 26 (1957), pp. 95-172.
[19] C. Sinestrari, The Riemann problem for an inhomogeneous conservation law without convexity,
Siam J. Math. Anal., 28, No. 1, (1997), pp. 109-135.
[20] C. Sinestrari, Asymptotic profile of solutions of conservation laws with source, Diff. and Integral Equations, 9, No. 3, (1996), pp. 499-525.
[21] M. Slemrod and A. Tzavaras, A limiting viscosity approach for the Riemann problem in isentropic gas dynamics, Ind. Univ. Math. J. 38 (1989), pp. 1047-1073.
[22] J. Smoller, Shock waves and reaction-dffusion equations, Springer, New York, 1983.
[23] A. Tzavaras, Waves interactions and variation estimates for self-similar zero viscosity limits in systems of conservation laws, Arch. Ration. Mech. Anal., 135 (1996), pp. 1-60.
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225-267.
指導教授 洪盟凱(John M. Hong) 審核日期 2011-1-19
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