In this paper, we cross the boundary between semigroup theory and general infinite-dimensional systems to bridge the isolated research activities in the two areas. Indeed, we first give a chronological history of the development of the semigroup approach for control theory. Second, we use the feedback theory to prove the well-posedness of a class of dynamic boundary problems. Third, the obtained results are applied to the well-posedness of neutral equations with non-autonomous past. We will also see that the strong connection between semigroup and control theories lies in feedback theory, where different kinds of perturbations appear. This article is part of the theme issue ‘Semigroup applications everywhere’.

中文翻译：

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进化方程适定性的反馈理论

在本文中，我们跨越了半群理论和一般无限维系统之间的界限，以弥合这两个领域的孤立研究活动。事实上，我们首先给出控制理论半群方法发展的时间顺序。其次，我们使用反馈理论来证明一类动态边界问题的适定性。第三，将所得结果应用于具有非自治过去的中性方程的适定性。我们还将看到半群理论和控制理论之间的紧密联系在于反馈理论，其中出现了不同类型的扰动。这篇文章是主题问题“无处不在的半组应用程序”的一部分。