非線性守恆律的擾動Riemann 問題的古典解

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：7

、訪客IP：3.140.185.123

姓名

周世偉(Shih-Wei Chou) 查詢紙本館藏

畢業系所

數學系

論文名稱

非線性守恆律的擾動Riemann 問題的古典解
(Classical Solution to the Perturbed Riemann Problem of Scalar Nonlinear Balance Law)

相關論文

★ 氣流的非黏性駐波通過不連續管子之探究	★ An Iteration Method for the Riemann Problem of Some Degenerate Hyperbolic Balance Laws
★ 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	★ 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

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

在本文裡我們學習非線性守恆律的擾動Riemann 問題的古典解之廣域存在性,使用特徵線的方法去建立擾動的Riemann問題的古典解,而且經由擾動的Riemann問題的極限獲得Riemann 問題的解。

摘要(英)

In this paper we study the global existence of classical solutions to the perturbed Riemann problem of scalar nonlinear balance law. The characteristic method is used to establish the existence of classical perturbed Riemann solutions. Moreover, the generalized solutions of Riemann problem to scalar balance law is obtained by taking the limit of perturbed Riemann solutions. Furthermore, we also obtain the self-similarity of generalized Riemann solutions (rarefaction waves) which enables us to apply Lax’’s method to the Riemann problem of scalar nonlinear balance laws.

關鍵字(中)

★ 非線性黎曼問題
★ 特徵線法
★ 守恆律

關鍵字(英)

★ Perturbed Riemann problems
★ Riemann problems
★ Nonlinear balance laws
★ Characteristic method
★ Conservation laws

論文目次

中文摘要………………………………………………………………i
英文摘要………………………………………………………………ii
圖目錄…………………………………………………………………iii
一. Introduction……………………………………………………2
二. Classical Solutions of Perturbed Riemann Problem………6
References……………………………………………………………20

參考文獻

C. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Ind. Univ. Math. J. (1977), 1097-1119.
C. Dafermos, Solutions of the Riemann problem for a class of conservation laws by the viscosity method, Arch. Ration. Mech. Anal.(1973), 1-9.
G. Dal Maso, P. LeFloch and F. Murat, Definition and weak
stability of nonconservative products, J. Math. Pure. Appl.,1995), 483-548.
J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math.,1956), 697-715.
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,2006), 515-549.
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 625-640.
E. Isaacson and B. Temple, Convergence of $2 imes 2$ by Godunov method for a general resonant nonlinear balance law, SIAM J. Appl.Math. 55 (1995), pp 625-640.
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.
S. Kruzkov, First order quasilinear equations with several space variables, Math. USSR Sbornik (1970), 217-273.
P. D. Lax, Hyperbolic system of conservation laws, II, Comm. Pure Appl. Math.,1957), 537-566.
T. P. Liu, The Riemann problem for general systems of conservation laws, J. Diff. Equations,1975), 218-234.
T. P. Liu, Quaslinear hyperbolic systems, Comm. Math. Phys.,1979), 141-172.
C. Mascia and C. Sinestrari, The perturbed Riemann problem for a balance law, Advances in Differential Equations, 1996-041.
O. A. Oleinik, Discontinuous solutions of nonlinear differential equations,Amer. Math. Soc. Transl. Ser. 2, (1957), 95-172.
C. Sinestrari, The Riemann problem for an inhomogeneous
conservation law without convexity, Siam J. Math. Anal., Vo28,No1, (1997), 109-135.
C. Sinestrari, Asymptotic profile of solutions of conservation laws with source, J. Diff. and Integral Equations, Vo9, No3,(1996), 499-525.
M. Slemrod and A. Tzavaras, A limiting viscosity approach for the Riemann problem in isentropic gas dynamics, Ind. Univ. Math. J. (1989), 1047-1073.
J. Smoller, Shock waves and reaction-dffusion equations, Springer,New York, 1983.
A. Tzavaras, Waves interactions and variation estimates for self-similar zero viscosity limits in systems of conservation laws, Arch. Ration. Mech. Anal., (1996), 1-60.
A. Volpert, The space BV and quasilinear equations, Maths. USSR Sbornik (1967), 225-267.

指導教授

洪盟凱(John M. Hong)

審核日期

2007-7-4

推文