<p style='text-indent:20px;'>In this paper, we obtain some stability results of systems corresponding to the coupling between a dissipative evolution equation (set in an infinite dimensional space) and an ordinary differential equation. Many problems from physics enter in this framework, let us mention dispersive medium models, generalized telegraph equations, Volterra integro-differential equations, and cascades of ODE-hyperbolic systems. The goal is to find sufficient (and necessary) conditions on the involved operators that garantee stability properties of the system, i.e., strong stability, exponential stability or polynomial one. We also illustrate our abstract statements for different concrete examples, where new results are achieved.</p>

中文翻译：

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耗散演化方程与常微分方程耦合的稳定性和渐近性质

<p style='text-indent:20px;'>在本文中，我们得到了对应于耗散演化方程（设置在无限维空间）和常微分方程之间耦合的系统的一些稳定性结果。物理学中的许多问题都进入了这个框架，让我们提到色散介质模型、广义电报方程、Volterra 积分-微分方程和 ODE-双曲系统的级联。目标是在涉及的算子上找到保证系统稳定性特性的充分（和必要）条件，即强稳定性、指数稳定性或多项式稳定性。我们还针对不同的具体示例说明了我们的抽象陈述，在这些示例中取得了新的结​​果。</p>