二階非線性守恆律的整體經典解

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：17

、訪客IP：3.144.238.20

姓名

李育誠(Yu-cheng Lee) 查詢紙本館藏

畢業系所

數學系

論文名稱

二階非線性守恆律的整體經典解
(Global Classical Solutions for the 2 × 2 Nonlinear Balance Laws)

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	★ 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

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)

在這篇論文中,我們討論二階非線性系統守恆律的整體經典解存在性.使用特徵線法和A uniform a priori estimate我們去建立整體經典解的存在條件.

摘要(英)

In this thesis, we consider the Cauchy problem of 2 × 2 nonlinear hyperbolic balance laws whose source terms consist of the integral of unknowns. Such nonlinear balance laws arise in, for instance, the compressible Euler-Poisson equations of gas dynamics in Lagrangian coordinate. We are concerned with the global existence of classical solutions to the Cauchy problem of such differential-integro systems. We extend the results by Ta-tsien Li for quasilinear hyperbolic systems to our nonlinear balance laws. The method in this thesis based on the following three steps: (1) the theory of local classical solutions, (2) uniform a priori estimate, (3) global existence or blow up of classical solutions. We find the transformation so that the 2 × 2 system for the first derivatives of Riemann invariants are de-coupled under this transformation. So, the characteristic method for scalar equations can be applied.

關鍵字(中)

★ 雙曲守恆律
★ 非線性守恆律
★ 柯西問題
★ 整體經典解
★ 特徵線法

關鍵字(英)

★ Nonlinear balance laws
★ Hyperbolic conservation laws
★ Characteristic method
★ Global classical solutions
★ Cauchy problem

論文目次

中文摘要.................................................ⅰ
英文摘要.................................................ⅱ
1. Introduction...........................................2
2. Homogeneous System.....................................4
3. Non-homogeneous System................................10
4. Perturbed p-System with Source Term in Integral Form..13
5. A Uniform a-Priori Estimate...........................15
6. The Construction of h and Q...........................21
References...............................................23

參考文獻

C. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Ind. Univ.Math. J., 26, pp.1097-1119, 1977.
C. Dafermos, Solutions of the Riemann problem for a class of conservation laws by the viscosity method, Arch. Ration. Meeh. Anal., 52, pp. 1-9, 1973.
C. Dafermos and L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dissipation, Indiana U. Math. Journal, 31,No.4, pp. 471-491, 1982.
G. Dal Maso, P. LeFloeh and F. Murat, Definition and weak stability of noneonservative products,J. Math. Pure. Appl., 74, pp. 483-548, 1995.
Ronald J. DiPerna, Measure-Valued Solutions to Conservation Laws,Arch. Ration. Meeh. Anal., 88 , No.3, pp. 223-270. 31, 1985
J. Glimm, Solutions in the large for nonlinear hyperbolic
systems of equations, Comm. Pure Appl. Math., 18, pp.697-715, 1965.
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, pp. 515-549, 2006.
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, pp.819-857, 2004.
J. M. Hong and P. G. LeFloch,A version of Glimm method based on generalized Riemann problem, Portugaliae Mathematica 64, Fasc. 2, pp. 199-236, 20007.
E. Isaacson and B. Temple, Convergence of 2 x 2 by Godunov
method for a general resonant nonlinear balance law,SIAM J.
Appl. Math.55, pp. 625-640, 1995.
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. Rozanovaed., Nova Press, 2004.
S. Kruzkov, First order quasilinear equations with several space variables,Math. USSR Sbornik, 10, pp. 217-243, 1970.
P. D. Lax, Hyperbolic system of conservation laws, II, Comm. Pure Appl.Math., 10, pp. 537-566, 1957.
P. G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form,Comm. Partial Differential Equations,13, pp. 669-727, 1988.
Ta-tsien Li, Global Classical solutions for quasilinear hyperbolic systems, Research in Applied Math.,Wiley Press.
Fagui Liu, Cauchy problem for quasilinear hyperbolic systems,Yellow River Conservancy Press.
T. P. Liu, The Riemann problem for general systems of conservation laws,J. Diff.Equations, 18, pp. 218-234, 1975.
T. P. Liu, Quaslinear hyperbolic systems,Comm. Math.Phys., 68, pp. 141-172,1979.
C. Mascia and C. Sinestrari, The perturbed Riemann problem for a balance law,Advances in Differential Equations, 2,pp. 779-810, 1997.
O. A. Oleinik,Discontinuous solutions of nonlinear differential equations,Amer. Math. Soc. Transl. Ser. 2, 26, pp. 95-172. 32, 1957.
C. Sinestrari, The Riemann problem for an inhomogeneous
conservation law without convexity, SIAM J. Math. Anal., 28,No.1, pp. 109135, 1997.
C. Sinestrari, Asymptotic profile of solutions of conservation laws with source, Diff. and Integral Equations, 9, No.3, pp. 499-525, 1996.
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., 135, pp. 1-60, 1996.
A. Volpert, The space BV and quasilinear equations,Maths. USSR Sbornik 2, pp. 225-267,1967

指導教授

洪盟凱(John M. Hong)

審核日期

2010-6-29

推文