We consider an abstract class of differential inclusions, which covers differential-algebraic and non-autonomous problems as well as problems with delay. Under weak assumptions on the operators involved, we prove the well-posedness of those differential inclusions in a pure Hilbert space setting. Moreover, we study the causality of the associated solution operator. The theory is illustrated by an application to a semistatic quasilinear variant of Maxwell's equations.

中文翻译：

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一类微分包含的适定性

我们考虑微分包含的抽象类，它涵盖微分代数和非自治问题以及延迟问题。在所涉及的算子的弱假设下，我们证明了在纯希尔伯特空间设置中那些微分包含的适定性。此外，我们研究了相关解算子的因果关系。该理论通过对麦克斯韦方程组的半静态拟线性变体的应用来说明。