双曲型仿射不变流的最优系统及群不变解
PDF下载 (634)沃维丰 1,杨淑心 1,黄 晴 2.双曲型仿射不变流的最优系统及群不变解[J].宁波大学学报(理工版),2017,30(3):36-41.DOI:
WO Wei-feng 1,YANG Shu-xin 1,HUANG Qing 2.Optimal system and group invariant solutions of a hyperbolic-type affine invariant flow[J].Journal of Ningbo University(Natural Science & Engineering Edition),2017,30(3):36-41.DOI:
| Title: | Optimal system and group invariant solutions of a hyperbolic-type affine invariant flow |
| 作者: | 沃维丰 1, 杨淑心 1, 黄 晴 2 |
| Author(s): | WO Wei-feng 1, YANG Shu-xin 1, HUANG Qing 2 |
| 关键词: | 双曲型仿射不变曲线流; 李点对称群; 最优系统; 对称约化; 群不变解 |
| Keywords: | 双曲型仿射不变曲线流; 李点对称群; 最优系统; 对称约化; 群不变解 |
| 分类号: | O175.27 |
| 文献标识码: | A |
| 摘要: | 利用李点对称群理论, 研究了双曲型仿射不变流的对称群, 构造了几何流对应的最优系统, 并利用最优系统对方程进行约化, 讨论了群不变解. |
| 参考文献 /References: | [1] CHOU K S, ZHU X P. The Curve Shortening Problem [M]. Boca Raton FL: Chapman & Hall/CRC, 2001:1-68. [2] QU C Z, HUANG Q. Symmetry reductions and exact solutions of the affine heat equation[J]. J Math Anal Appl, 2008, 346:521-530. [3] DONG Z Z, CHEN Y, KONG D X. Symmetry reduction and exact solutions of a hyperbolic Monge-Ampere equation[J]. Chinese Annals of Mathematics, 2012, 33B(2): 309-316. [4] CHOU K S, LI G X. Optimal systems and invariant solutions for the curve shortening problem[J]. Communi- cations in Analysis & Geometry, 2002, 10(2):241-274. [5] WO W F, MA F Y, QU C Z. A hyperbolic-type affine invariant curve flow[J]. Communications in Analysis & Geometry, 2014, 22(2):219-245. [6] OVSIANNIKOV L V. Group analysis of differential equations[M]. New York: Academic Press, 1982:68-339. [7] OLVER P J. Applications of Lie Groups to Differential Equations[M]. New York: Springer, 1998:75-238. |
| 备注/Memo: | 收稿日期: 2016-09-21. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（11201249）; 浙江省自然科学基金（LY16A010002）. 第一作者: 沃维丰（1981-）, 女, 浙江宁波人, 讲师, 主要研究方向: 偏微分方程. E-mail: woweifeng@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
