A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modelled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.

中文翻译：

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与开关DAE耦合的线性双曲PDE的分布式解决方案框架

针对由边界条件耦合的线性双曲偏微分方程和切换微分代数方程（DAE）组成的系统，开发了一种分布式解决方案框架。然后，根据开关延迟DAE来表征唯一的可溶解性。通过以电报方程式建模的电力线示例说明了该理论，该电报线方程通过开关变压器耦合，其中仿真确定了预测的脉冲解。