具有内阻尼和边界反馈控制的一类Euler-Bernoulli梁方程的Riesz基性质  

On Riesz Basis Property of Euler-Bernoulli Beam Equation with Internal Damping and Boundary Feedback

作　　者：陶宸 梅占东 TAO Chen;MEI Zhan-dong(School of Mathematics and Statistics,Xi’an Jiaotong University,Xi'an 710049,China)

机构地区：[1]西安交通大学数学与统计学院,陕西西安710049

出　　处：《数学的实践与认识》2022年第5期167-172,共6页Mathematics in Practice and Theory

基　　金：陕西省自然科学基金(2018JM1051,2014JQ1017);中央高校基础研究经费(xjj2017177);国家自然科学基金(11301412)。

摘　　要：考虑一类具有内阻尼和边界反馈控制的一维Euler-Bernoulli梁方程.中导出系统特征值和特征函数的渐近表达式,并且通过Riesz基生成定理的优点,证明该系统是一个Riesz系统,即该系统存在一列广义特征函数构成能量状态空间的一组Riesz基.从而,系统的谱决定增长条件成立,进而证明系统的指数稳定性.This paper is concerned with a one-dimensional Euler-Bernoulli beam equation with internal damping and boundary feedback.In this paper,the asymptotic expressions of the eigenvalues and eigenfunctions of the system are derived and by virtue of Riesz basis generation theorem,it is proved that this system is a Riesz system,which means there is a sequence of generalized eigenfunctions of this system forming a Riesz basis for the energy state Hilbert space.Hence,spectrum-determined growth condition holds for the system and therefore,the exponential stability of the system is verified.

关 键 词：Euler-Bernoulli梁方程 RIESZ基 稳定性 C_(0)半群 

分 类 号：O175[理学—数学]