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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/19305完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 夏俊雄 | |
| dc.contributor.author | Po-Wei Li | en |
| dc.contributor.author | 李柏緯 | zh_TW |
| dc.date.accessioned | 2021-06-08T01:52:55Z | - |
| dc.date.copyright | 2016-09-13 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-07-20 | |
| dc.identifier.citation | [1] C. Bardos, G. Lebeau, and J. Rauch. Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM journal on control and optimization, 30(5):1024–1065, 1992.
[2] A. Bensoussan. An introduction to the hilbert uniqueness method. In Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems, pages 184–198. Springer, 1993. [3] J.-M. Coron. Control and nonlinearity. Number 136. American Mathematical Soc., 2007. [4] G. E. Fasshauer, B. P. Rynne, and M. A. Youngson. Linear functional analysis., 2010. [5] A. E. Ingham. Some trigonometrical inequalities with applications to the theory of series. Mathematische Zeitschrift, 41(1):367–379, 1936. [6] V. Komornik and V. Gattulli. Exact controllability and stabilization. the multiplier method. SIAM Review, 39(2):351–351, 1997. [7] J. L. Lions. Contrôlabilité exacte perturbations et stabilisation de systèmes distribués(tome 1, contrôlabilité exacte. tome 2, perturbations). Recherches en mathematiques appliquées, 1988. [8] A. Pazy. Semigroups of linear operators and applications to partial differential equations, volume 44. Springer Science & Business Media, 2012. [9] L. Rosier. Exact boundary controllability for the korteweg-de vries equation on a bounded domain. ESAIM: Control, Optimisation and Calculus of Variations, 2:33-55, 1997. [10] W. Rudin. Principles of mathematical analysis, volume 3. McGraw-Hill New York, 1964. [11] D. L. Russell and B. Y. Zhang. Controllability and stabilizability of the third-order linear dispersion equation on a periodic domain. SIAM journal on control and optimization, 31(3):659–676, 1993. [12] J. Simon. Compact sets in the spacel p (o, t; b). Annali di Matematica pura ed applicata, 146(1):65–96, 1986. [13] E. M. Stein and R. Shakarchi. Princeton lectures in analysis. Princeton University Press, 2003. [14] K. Yosida. Functional analysis. reprint of the sixth (1980) edition. classics in mathematics. Springer-Verlag, Berlin, 11:14, 1995. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/19305 | - |
| dc.description.abstract | 在這篇文章中我們探討控制理論之Lionel Rosier 定理。控制性概括
來說: 給定初始狀態及終端狀態，我們希望找到一個控制函數來引導此 系統，使得給定初始值之系統能確保終端時刻的狀態是我們所要的。 而此篇研究的對象為KdV 方程。 | zh_TW |
| dc.description.abstract | In this paper we shall survey Lionel Rosier’s theorem ([9]) about control
theory. Roughly speaking, by controllability ([3]) we mean: given the initial state and the terminal state, we want to find a control function which can steer the system, such that the system with initial data can ensure the terminal state is the desired. In this paper, we study the KdV equation. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T01:52:55Z (GMT). No. of bitstreams: 1 ntu-105-R01221026-1.pdf: 633609 bytes, checksum: 9ef367c6e9cc8da16e797fd24fe27c9f (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 口試委員會審定書 ... iii
摘要 ... v Abstract vii 1 Introduction and Main Theorems ... 1 2 Exact Boundary Controllability of Linear KdV Equation via Controlling the Boundary Conditions ...5 3 Exact Boundary Controllability of Linear KdV Equation via Controlling the y_x(t,L) Term ... 15 4 Exact Boundary Controllability of Non-linear KdV Equation on a Bounded Domain ... 27 5 Conclusion ... 33 Bibliography ... 35 | |
| dc.language.iso | en | |
| dc.title | KdV方程在有界域內的精準邊界控制性之探討 | zh_TW |
| dc.title | A Survey on Exact Boundary Controllability for the Korteweg-De Vries Equation on a Bounded Domain | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 洪盟凱,鄭經 | |
| dc.subject.keyword | KdV 方程,Hilbert 唯一性方法,Fourier 轉換,半群,Lax- Milgram 定理, | zh_TW |
| dc.subject.keyword | KdV equation,H.U.M.,Fourier transform,semigroup,Lax-Milgram theorem, | en |
| dc.relation.page | 36 | |
| dc.identifier.doi | 10.6342/NTU201601108 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2016-07-20 | |
| 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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