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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58687完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 夏俊雄 | |
| dc.contributor.author | Shih-Hsin Chen | en |
| dc.contributor.author | 陳世昕 | zh_TW |
| dc.date.accessioned | 2021-06-16T08:25:45Z | - |
| dc.date.available | 2015-07-29 | |
| dc.date.copyright | 2014-07-29 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-01-21 | |
| dc.identifier.citation | [1] C. Cao and E. S. Titi. Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics. Annals of Mathematics, pages 245–267, 2007.
[2] G. Da Prato, A. Debussche, and R. Temam. Stochastic burgers’ equation. Nonlinear Differential Equations and Applications NoDEA, 1(4):389–402, 1994. [3] L. C. Evans. Partial differential equations. graduate studies in mathematics. American mathematical society, 2, 1998. [4] C.-H. Hsia and M.-C. Shiue. On the asymptotic stability analysis and the existence of time-periodic solutions of the primitive equations. 2012. [5] G. Łukaszewicz, E. Ortega-Torres, and M. Rojas-Medar. Strong periodic solutions for a class of abstract evolution equations. Nonlinear Analysis: Theory, Methods & Applications, 54(6):1045–1056, 2003. [6] T. T. Medjo. Existence and uniqueness of strong periodic solutions of the primitive equations of the ocean. 2010. [7] E. Parkes and B. Duffy. Travelling solitary wave solutions to a compound kdvburgers equation. Physics Letters A, 229(4):217–220, 1997. 33 [8] Z.-S. She, E. Aurell, and U. Frisch. The inviscid burgers equation with initial data of brownian type. Communications in mathematical physics, 148(3):623–641, 1992. [9] Y. G. Sinai. Statistics of shocks in solutions of inviscid burgers equation. Communications in mathematical physics, 148(3):601–621, 1992. [10] R. Temam. Navier–Stokes Equations. American Mathematical Soc., 1984. [11] M. Wang. Exact solutions for a compound kdv-burgers equation. Physics Letters A, 213(5):279–287, 1996. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58687 | - |
| dc.description.abstract | 在一維的開區間上，我們考慮一個帶有黏滯項與時間週期的外力的Burgers'型方程式，且方程式滿足狄利克雷邊界條件。我們將利用伽遼金方法與Schaefer不動點定理，證明時間週期解的存在性； 並證明在某種程度夠小的時間週期外力下，此時間週期解是唯一的，且滿足$H^1$漸進穩定。 | zh_TW |
| dc.description.abstract | We consider the Burgers' type equation with a viscosity term and a time periodic force defined on a one dimensional open interval domain with Dirichlet boundary condition. We prove the existence of the time periodic solution with some regular time periodic force by using Galerkin method and Schaefer's fixed point theorem, and moreover, we show that this time periodic solution is unique and globally asymptotically stable in $H^1$ sense under additional condition with small force in some sense. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T08:25:45Z (GMT). No. of bitstreams: 1 ntu-103-R00221002-1.pdf: 816253 bytes, checksum: 9fec888d4ae0fced3622a712bb1a7827 (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | Table of Contents
口試委員會審定書 i 誌謝 ii 中文摘要 iv 英文摘要 v 1 Introduction 1 2 Preliminary 3 2.1 The Model Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Fundamental Functional Space . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Space With Time Evolution . . . . . . . . . . . . . . . . . . . . 5 2.3 Mathematics Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Approximate Solution and Prior Estimate 12 3.1 Galrekin Method and L2 Estimate . . . . . . . . . . . . . . . . . . . . . 12 3.2 H1 and High Order Estimate . . . . . . . . . . . . . . . . . . . . . . . . 19 4 Existence, Uniqueness and Stability of Time Periodic Solution 25 4.1 Existence and Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 H1 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 References 33 | |
| dc.language.iso | en | |
| dc.subject | 伯格斯方程 | zh_TW |
| dc.subject | 週期解 | zh_TW |
| dc.subject | time periodic solution | en |
| dc.title | Burgers型方程的週期解 | zh_TW |
| dc.title | Time Periodic Solutions of a Burgers' Type Equation | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳俊全,鄭經? | |
| dc.subject.keyword | 週期解,伯格斯方程, | zh_TW |
| dc.subject.keyword | time periodic solution, | en |
| dc.relation.page | 34 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-01-21 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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