We show how strongly continuous semigroups can be associated with evolutionary equations. For doing so, we need to define the space of admissible history functions and initial states. Moreover, the initial value problem has to be formulated within the framework of evolutionary equations, which is done by using the theory of extrapolation spaces. The results are applied to two examples. First, differential-algebraic equations in infinite dimensions are treated and it is shown, how a \(C_{0}\)-semigroup can be associated with such problems. In the second example we treat a concrete hyperbolic delay equation.

中文翻译：

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半群和进化方程

我们展示了连续半群与进化方程的关联程度。为此，我们需要定义可接受的历史函数和初始状态的空间。此外，初始值问题必须在进化方程的框架内制定，这是通过使用外推空间理论来完成的。结果应用于两个示例。首先，处理无穷维的微分代数方程，并说明\(C_{0}\) -半群如何与此类问题相关联。在第二个例子中，我们处理一个具体的双曲延迟方程。