In this paper, we study stability for a Schrödinger equation interacted by an Euler‐Bernoulli beam equation with Kelvin‐Voigt damping through weak boundary connections. It is shown that the whole coupled system is well‐posed. With a careful spectral analysis, it is shown that the system operator of the closed‐loop system is not of compact resolvent and the spectrum consists of three branches. By means of asymptotic analysis, the asymptotic expressions of eigenfunctions are obtained. The Riesz basis property and exponential stability of the system are concluded by comparison method in Riesz basis approach. Finally, we show that the associated C₀‐semigroup is of Gevery class $\delta >4$ which is a remarkable difference with the related literature.

中文翻译：

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Schrödinger方程通过开尔文-Voigt阻尼梁方程的边界连接的稳定和正则传递

在本文中，我们研究了通过弱边界连接，与具有开尔文-沃格特阻尼的欧拉-伯努利梁方程相互作用的薛定ding方程的稳定性。结果表明，整个耦合系统状态良好。通过仔细的频谱分析，可以看出闭环系统的系统运算符不是紧凑的分解体，并且频谱由三个分支组成。通过渐近分析，获得本征函数的渐近表达。通过Riesz基方法的比较方法，得出了系统的Riesz基性质和指数稳定性。最后，我们证明关联的C _0-半群属于Gevery类$\delta >4$ 这与相关文献有显着差异。