学术
非线性弹性杆中的应变孤波
谢永钦[1,2] 杨莉[2] 秦桂香[2]
[1]兰州大学数学与统计学院,甘肃兰州730000 [2]长沙理工大学数学与计算科学学院,湖南长沙410076
摘 要:
当非线性弹性杆承受平向拉、压突加载荷时产生几何弥散效应后,杆中可能形成应变孤波.本文对该问题的数学模型进行分析,利用Galerkin逼近方法结合能量估计得到了该应变孤波存在的充分条件,并且证得应变孤波解是唯一的,且连续依赖于初始值.改进了已有的结果.[著者文摘]
关 键 词:
文章出处:
《湖南大学学报：自然科学版》-2007年34卷5期 -58-61页
栏目信息:
文献标识码:
A
文章编号:
1000-2472（2007）05-0058-04
Strain Solitary Waves in a Nonlinear Elastic Rod
XIE Yong-qin, YANG Li, QIN Gui-xiang （1.School of Mathematics and Statistics, Lanzhou Univ, Lanzhou, Gansu 730000, China; 2.School of Mathematics and Computation, Changsha Univ of Science and Technology, Changsha,Hunan 410076, China）
Abstract:
This paper analyzed the mathematical model of the strain solitary waves, which were possibly formed after the Geometry dispersion effect was produced when the nonlinear elastic rod was loaded with sudden bearing pulling or pressing. We have obtained the sufficient conditions for the existence of the strain solitary waves by means of Galerkin methods and energy estimation. And we have proved that the strain solitary waves depend on the original value uniquely and continuously, which improves the existing results.[著者文摘]
Key words:
strain solitary waves; Galerkin methods; global solutions
基金资助:
国家自然科学基金资助项目（10571178）;湖南省教育厅资助项目（06C103）
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