一些退化擬線性波動方程的解的性質.

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：45

、訪客IP：3.146.65.212

姓名

許維文(Wei-wen Hsu) 查詢紙本館藏

畢業系所

數學系

論文名稱

一些退化擬線性波動方程的解的性質.
(The Behavior of Solutions for Some Degenerate Quasilinear Wave Equations.)

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
★ 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	★ 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)

我們的論文主要在探討一些退化擬線性波動方程的解的性質。首先我們先探討線性退化波動方程，我們由d’’Almbert formula 得到了解具有 L1-stability的性質。而在非線性的例子當中，我們由雙曲線型守恆律的 Lax method 及 Glimm method 得到了柯西黎曼問題在第一階段的估計解。並且在我們的論文當中，我們將會由一些例子，來探討退化擬線性波動方程的估計解的總變異量是否會接近無限大。

摘要(英)

In this paper we consider the Cauchy problem of some degenerate quasilinear wave equations. We first study the behavior of solutions to the linear degenerate wave equation. We obtain the -stability of solutions for the linear case just by the d’’Almbert formula. To the nonlinear degenerate case, the Lax method and Glimm method in hyperbolic systems of conservation laws are used to construct the approximate solution of Cauchy problem in the first time step. As we demonstrate in this paper, the total variation of approximate solution may go to infinity due to the degeneracy of equation. We will do the case study for the behavior of solutions for some particular case of degenerate quasilinear wave equations.

關鍵字(中)

★ 黎曼問題
★ 退化擬線性波動方程
★ 雙曲線型守恆律系統

關鍵字(英)

★ Riemann problem
★ hyperbolic systems of conservation laws
★ Degenerate quasilinear wave equations

論文目次

Contents
1.Introduction..........................................2
2.Linear degenerate wave equations......................3
3.Nonlinear degenerate wave equations...................6
4.References...........................................19

參考文獻

[1]C. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Ind. Univ. Math. J. 26 (1977), 1097-1119.
[2]C. Dafermos, Solutions of the Riemann problem for a class of conservation lawsby the viscosity method, Arch. Ration. Mech. Anal., 52 (1973), 1-9.
[3]G. Dal Maso, P. LeFloch and F. Murat, Definition and weak
stability of nonconservative products, J. Math. Pure. Appl., 74 (1995), 483-548.
[4]J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18 (1956), 697-715.
[5]J. M. Hong, An extension of Glimm's method to inhomogeneous strictly hyperbolic systems of conservation laws by "weaker than weaker" solutions of the Riemann problem, J. Diff. Equations, 222 (2006), 515-549.
[6]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.
[7]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.
[8]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.
[9]S. Kruzkov, First order quasilinear equations with several space variables, Math. USSR Sbornik 10 (1970), 217-273.
[10]P. D. Lax, Hyperbolic system of conservation laws, II, Comm. Pure Appl. Math., 10 (1957), 537-566.
[11]T. P. Liu, The Riemann problem for general systems of conservation laws, J. Diff. Equations, 18 (1975), 218-234.
[12]T. P. Liu, Quaslinear hyperbolic systems, Comm. Math. Phys., 68 (1979), 141-172.
[13]C. Mascia and C. Sinestrari, The perturbed Riemann problem for a balance law, Advances in Differential Equations, 1996-041.
[14]O. A. Oleinik, Discontinuous solutions of nonlinear differential equations, Amer. Math. Soc. Transl. Ser. 2, 26 (1957), 95-172.
[15]C. Sinestrari, The Riemann problem for an inhomogeneous
conservation law without convexity, Siam J. Math. Anal., Vo28, No1, (1997), 109-135.
[16]C. Sinestrari, Asymptotic profile of solutions of conservation laws with source, J. Diff. and Integral Equations, Vo9, No3,(1996), 499-525.
[17]M. Slemrod and A. Tzavaras, A limiting viscosity approach for the Riemann problem in isentropic gas dynamics, Ind. Univ. Math. J. 38 (1989), 1047-1073.
[18]J. Smoller, Shock waves and reaction-dffusion equations, Springer, New York, 1983.
[19]A. Tzavaras, Waves interactions and variation estimates for self-similar zero viscosity limits in systems of conservation laws, Arch. Ration. Mech. Anal., 135 (1996), 1-60.
[20]A. Volpert, The space BV and quasilinear equations, Maths. USSR Sbornik 2 (1967), 225-267.

指導教授

洪盟凱(John M. Hong)

審核日期

2007-7-4

推文