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| 研究生： |
陳滙勝 Hui-Sheng Chen |
|---|---|
| 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 |
| 指導教授： |
洪盟凱
John M. Hong |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 畢業學年度： | 96 |
| 語文別： | 英文 |
| 論文頁數： | 19 |
| 中文關鍵詞： | 極限週期 、線性BBM方程 、線性KdV方程 |
| 外文關鍵詞： | linear KdV equation, linear BBM equation, Eventual periodicity |
| 相關次數： | 點閱：6 下載：0 |
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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。
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.
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[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.
