簡易檢索 / 詳目顯示
| 研究生： |
陳汛汯 Chen, Hsun-Hung |
|---|---|
| 論文名稱： |
二維與三維的波動方程之比較 Comparison between 2-dimensional and 3-dimensional wave equations |
| 指導教授： |
吳恭儉
Wu, Kung-Chien |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系應用數學碩博士班 Department of Mathematics |
| 論文出版年： | 2024 |
| 畢業學年度： | 112 |
| 語文別： | 英文 |
| 論文頁數： | 42 |
| 中文關鍵詞： | 波動方程式 、d'Alembert 公式 、Kirchhoff's 公式 、Poisson's公式 |
| 外文關鍵詞： | wave equations, d'Alembert formula, Kirchhoff's formula, Poisson's formula |
| 相關次數： | 點閱：52 下載：4 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
自然界中有很多現象與波有關，用偏微分方程描述此類現象，稱為波動方程式。在這個論文中，我將參考[1]並推導出一維、二維和三維波動方程的解。我們會在二維和三維的波動方程中觀察到一些不同的結果，並將一些結果推廣到更高維度的情況。
In nature, there are many phenomena related to waves, so we hope to describe such phenomena with partial differential equations. The equations described in this way are called wave equations.
In this thesis, I will refer to [1] and derive the solutions of one, two and three-dimensional wave equations. we will observe some different results about these solutions especially on two and three dimensional and extend the results to the higher dimensional cases.
[1] L. C. Evans. Partial differential equations, volume 19 of Grad. Stud.Math. American Mathematical Society, Providence, RI, second edition,2010. MR2597943, Zbl:1194.35001, doi:10.1090/gsm/019.
[2] W. A. Strauss. Partial differential equations: An introduction. JohnWiley & Sons, Ltd., Chichester, second edition, 2008.MR2398759,Zbl:1160.35002.
[3] R. L. Wheeden and A. Zygmund. Measure and integral. An introduction to real analysis. Pure Appl. Math. CRC Press, Boca Raton, FL, second edition, 2015.MR3381284, Zbl:1326.26007.
[4] W. Rudin. Real and complex analysis. McGraw-Hill Book Co., New York, third edition, 1987. MR0924157,Zbl:0925.00005.
[5] B. Yan. MTH849-Partial Differential Equations. Department of Mathematics.Michigan State University.
[6] J.Kinnunen. Partial Differential Equations. Department of Mathematics and Systems Analysis. Aalto University.
[7] V.Barbu. Partial Differential Equations and Boundary Value Problem.
校內：立即公開校外：立即公開