This paper is devoted to the study of the robustness properties of the 1-D wave equation for an elastic vibrating string under four different damping mechanisms that are usually neglected in the study of the wave equation: (i) friction with the surrounding medium of the string (or viscous damping), (ii) thermoelastic phenomena (or thermal damping), (iii) internal friction of the string (or Kelvin-Voigt damping), and (iv) friction at the free end of the string (the so-called passive damper). The passive damper is also the simplest boundary feedback law that guarantees exponential stability for the string. We study robustness with respect to distributed inputs and boundary disturbances in the context of Input-to-State Stability (ISS). By constructing appropriate ISS Lyapunov functionals, we prove the ISS property expressed in various spatial norms.

本文致力于研究在四种不同的阻尼机制下弹性振动弦的一维波动方程的稳健性，这四种不同的阻尼机制在波动方程的研究中通常被忽略：（i）与周围介质的摩擦弦（或粘性阻尼），（ii）热弹性现象（或热阻尼），（iii）弦的内部摩擦（或开尔文-福格特阻尼），以及（iv）弦自由端的摩擦（所谓的称为被动阻尼器）。被动阻尼器也是最简单的边界反馈法则，可确保弦的指数稳定性。我们在输入状态稳定性 (ISS) 的背景下研究分布式输入和边界扰动的稳健性。通过构造适当的 ISS Lyapunov 泛函，我们证明了以各种空间规范表示的 ISS 属性。