...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Mathematische Nachrichten >On the completeness of root vectors of a certain class of differential operators
【24h】

On the completeness of root vectors of a certain class of differential operators

机译：一类微分算子根向量的完备性

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The present paper is the first one in a series of two papers devoted to a unified approach to the problem of completeness of the generalized eigenvectors (the root vectors) for a specific class of linear non-selfadjoint unbounded differential operators. The list of the problems for which such operators are the dynamics generators includes the following: (a) initial boundary-value problem (IBVP) for a non-homogeneous string with both distributed and boundary damping; (b) IBVP for small vibrations of an ideal filament with dissipative boundary condition at one end and with a heavy load at the other end; (c) IBVP for a three-dimensional damped wave equation with spherically symmetric coefficients and both distributed and boundary damping. In the second paper of the series the following problems will be considered: (a) IBVP for a system of two coupled hyperbolic equations constituting a Timoshenko beam model with variable coefficients and boundary damping; (b) IBVP for a coupled Euler–Bernoulli and Timoshenko beam model with boundary energy dissipation (the model known in engineering literature as bending-torsion vibration model); (c) IBVP for a system of two Timoshenko beams coupled through linear Van der Waals forces. The model of (c) describes vibrational motion of a double-walled carbon nanotube. In all of the above cases, the result has been obtained by using Krien’s Theorem on completeness of root vectors of a dissipative operator with a nuclear imaginary part. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
机译：本文是两篇系列文章中的第一篇，该系列文章致力于针对特定类别的线性非自伴无界微分算子的广义特征向量（根向量）的完整性问题的统一方法。这些算子是动力学生成器的问题列表包括：（a）具有分布阻尼和边界阻尼的非均质弦的初始边界值问题（IBVP）； （b）IBVP用于理想的灯丝的小振动，其一端具有耗散的边界条件，而另一端具有较大的负载； （c）具有球形对称系数，分布和边界阻尼的三维阻尼波方程的IBVP。在该系列的第二篇论文中，将考虑以下问题：（a）IBVP用于两个耦合双曲方程组的系统，这些方程组构成具有可变系数和边界阻尼的Timoshenko梁模型； （b）具有边界能量耗散的欧拉-伯努利和蒂莫申科耦合梁模型的IBVP（在工程文献中称为弯曲扭转振动模型的模型）； （c）通过线性范德华力耦合的两个Timoshenko梁的系统的IBVP。 （c）的模型描述了双壁碳纳米管的振动运动。在上述所有情况下，都使用Krien定理对具有核虚部的耗散算子的根向量的完备性进行了获得。 ©2011 WILEY-VCH Verlag GmbH＆Co. KGaA，Weinheim

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号