BBM與KdV方程初始邊界問題解的週期性

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：98

、訪客IP：3.140.188.95

姓名

陳滙勝(Hui-Sheng Chen) 查詢紙本館藏

畢業系所

數學系

論文名稱

BBM與KdV方程初始邊界問題解的週期性
(Eventual Periodicity of Solutions to the Linear Generalized BBM and KdV Equations in the Quarter Plane)

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
★ 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)

在這篇論文，我們探討線性BBM和KdV方程對於初始邊界問題解的週期性。根據[10]的方法，我們對線性BBM和KdV方程作奇函數擴充及偶函數擴充並藉由傅利葉轉換求得BBM和KdV方程的解，最後並探討BBM和KdV方程的週期性。

摘要(英)

In this paper we study the eventual periodicity of solutions to the initial-boundary value problem for the linear generalized BBM-Burgers and KdV-Burgers equation in the quarter plane with periodic boundary data and force term. We derive a representation formula for solutions to the equations by the Fourier transform thought the odd and even extension. Finial, we rigorously establish the eventual periodicity of these solutions.

關鍵字(中)

★ 極限週期
★ 線性BBM方程
★ 線性KdV方程

關鍵字(英)

★ linear KdV equation
★ linear BBM equation
★ Eventual periodicity

論文目次

中文摘要 ........................................................................................i
英文摘要 .......................................................................................ii
Contents ........................................................................................iii
Introduction ....................................................................................1
2. Linear generalized BBM equation ...............................................3
2.1 Representation of solutions to BBM equation .........................3
2.2 Eventual periodicity of BBM equation.....................................9
3. Linear generalized KdV equation...............................................11
3.1 Representation of solutions to KdV equation..........................11
3.2 Eventual periodicity of KdV equation.....................................15
References.......................................................................................16
Appendix.........................................................................................17

參考文獻

[1] C.J. Amick, J.L. Bona and M.E. Schonbek, Decay of solutions of some nonlinear wave equations, J. Di . Eq. 81 (1989), 1-49.
[2] T. B. Benjamin, J. L. Bona, J. J. Mahony, Model Equations for Long Waves in Nonlinear Dispersive Systems, Philos. Royal Soc. London Series A, 272, (1972), 47-78.
[3] B. Boczar-Karakiewicz, J.L. Bona and D. Cohen, Interaction of shallow-water waves and bottom topography, In Dynamical problems in continuum physics, IMA Series in Mathematics and Its Aplications, 4, Springer-Verlag (1987), 131-176.
[4] B. Boczar-Karakiewicz, J.L. Bona and B. Pelchat, Interaction of internal waves with the sea bed on continental shelves, Continental Shelf Res. 11 (1991), 1181-1197.
[5] J.L. Bona, H. Chen, S. Sun and B. Zhang, Comparison of quarter-plane and two-point boundary value problems: the BBM-equation, Discrete Contin. Dyn. Sys. 13 (2005), 921-940.
[6] J.L. Bona and L. Luo, Initial-boundary value problems for model equations for the propagation of long waves, in: G. Gerrayra, G. Goldstein and F. Neubrander (Ed.), Lecture Notes in Pure and Appl. Math., 168, Dekker, New York, (1995), 65-94.
[7] J.L. Bona, W.G. Pritchard and L.R. Scott, An evaluation of a model equation for water waves, Philos. Royal Soc. London Series A 302 (1981), 457-510.
[8] J.L. Bona, S. Sun and B.-Y. Zhang, Forced oscillations of a damped Korteweg-de Vries equation in a quarter plane, Commun. Contemp. Math. 5 (2003), 369-400.
[9] J.L. Bona and J.Wu, Temporal growth and eventual periodicity for dispersive wave equations in a quarter plane, to appear in Discrete Contin. Dyn. Sys.
[10] J. M. Hong, J. Wu and J.-M. Yuan, Explicit solution representation for the BBM equation in a quarter plane and the eventual periodicity.
[11] E.H. Lieb and M. Loss, Analysis (second edition), American Mathematical Society, Providence, RI (2001).
[12] J. Shen, J. Wu and J.-M. Yuan, Eventual periodicity for the KdV equation on a half-line, Physica D 227 (2007), 105-119.

指導教授

洪盟凱(John M. Hong)

審核日期

2008-7-9

推文