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https://ah.lib.nccu.edu.tw/handle/140.119/51309| 題名: | 時間刻度下偏動態算子的極大值定理 The maximum principles for the partial dynamic operators on time scales |
作者: | 陳家盛 Chen, Chia Sheng |
貢獻者: | 符聖珍 陳家盛 Chen, Chia Sheng |
關鍵詞: | 時間刻度 動態算子 極大值定理 |
日期: | 2010 | 上傳時間: | 5-Oct-2011 | 摘要: | 在這篇論文裡，我們要討論的是在多維度的時間刻度下橢圓型動態算子和拋物型動態算子的極大值定理，並藉此得到一些應用。事實上，我們是將微分方程及差分方程裡的極大值定理推廣至所謂的動態方程中。 In this thesis, we establish the maximum principles for the elliptic dynamic operators and parabolic dynamic operators on multi-dimensional time scales, and apply it to obtain some applications. Indeed, we extend the maximum principles on differential equations and difference equations to the so-called dynamic equations. |
參考文獻: | [1]M. Protter, H. Weinberger,Maximum Principles in Differential Equations,Prentice-Hall, New Jersey, (1967). [2]H. Kuo, N. Trudinger,On the discrete maximum principle for parabolic difference operators,Math. Model. Numer. Anal. 27 (1993) 719-737. [3]G. David, N.S. Trudinger,Elliptic partial differential equations of second order,Berlin, New York: Springer- Verlag, (1977). [4]P. Stehlik, B. Thompson,Maximum principles for second order dynamic equations on time scales,J. Math. Anal. Appl. 331 (2007) 913-926. [5]P. Stehlik,Maximum principles for elliptic dynamic equations,Mathematical and Computer Modelling 51 (2010) 1193-1201. [6]R.P. Agarwal and M. Bohner,Basic calculus on time scales and some of its applications,Results Math. 35 (1999) 3- 22. [7]M. Bohner and A. Peterson,Dynamic Equation on Time Scales, An Introduction with Application,Birkhauser, Boston (2001). [8]M. Bohner and A. Peterson,Advances in Dynamic Equation on Time Scales,Birkhauser, Boston (2003). [9]B. Jackson,Partial dynamic equations on time scales,J. Comput. Appl. Math. 186 (2006) 391-415. |
描述: | 碩士 國立政治大學 應用數學研究所 97751014 99 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0097751014 | 資料類型: | thesis |
| Appears in Collections: | 學位論文 |
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| File | Size | Format | |
|---|---|---|---|
| 101401.pdf | 830.82 kB | Adobe PDF2 | View/Open |
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