has now appeared and is available as open access.
Borsche, Raul; Kocoglu, Damla; Trenn, Stephan
A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs Journal Article
In: Mathematics of Control, Signals, and Systems (MCSS), vol. 32, pp. 455-487, 2020, (Open Access).
A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations (PDEs) 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 modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.