SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 2174-2194, January 2021.
We study the semigroup associated to the Euler--Bernoulli beam equation with localized (discontinuous) dissipation. We assume that the beam is composed of three components: elastic, viscoelastic of Kelvin--Voigt type, and thermoelastic parts. We prove that this model generates a semigroup of Gevrey class that in particular implies the exponential stability of the model. To our knowledge, this is the first positive result giving increased regularity for the Euler--Bernoulli beam with localized damping.

中文翻译：

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Gevrey 类局部耗散欧拉--伯努利梁方程

SIAM Journal on Control and Optimization，第 59 卷，第 3 期，第 2174-2194 页，2021 年 1 月。
我们研究与具有局部（不连续）耗散的 Euler--Bernoulli 梁方程相关的半群。我们假设梁由三个分量组成：弹性、开尔文-福伊特型粘弹性和热弹性部分。我们证明该模型生成 Gevrey 类的半群，特别暗示了模型的指数稳定性。据我们所知，这是第一个为具有局部阻尼的欧拉-伯努利梁增加规律性的积极结果。