星形热弹性网络系统的稳定性及Riesz基性质

Stability and Riesz Basis of a Star-shaped Network of Thermoelasticities

研究了一类星形弹性网络系统在热效应影响以及边界反馈作用下的稳定性问题及系统相应(广义)特征向量的Riesz基性质.基于Green和Naghdi第二类热弹性理论,假设在该热弹性系统中热以有限波速传播,并且在传播过程中无能量耗散.证明了该热弹性网络系统能量渐近衰减到零.并进一步通过系统算子谱分析,讨论得出该系统算子的(广义)特征向量构成状态空间的一组Riesz基.

In this paper, we consider the stability and Riesz basis property of a star-shaped network of elastic strings with thermal effects and boundary feedback controls. The heat conduction in this system is decribed by the theory of thermoelasticity of type II proposed by Green and Naghdi, which is also known as ＂thermoelasticity without dissipation＂. We show that the total energy of this system decays to zero asymptotically. Moreover, we prove that there is a sequence of （generalized） eigenvectors of the system operator forming a Riesz basis with parentheses for the state space.