Finally we have published our key theoretical paper four our DFG-project “Coupling hyperbolic PDEs with switched DAEs: Analysis, numerics and application to blood flow models”:
Mathematics of Control, Signals, and Systems (MCSS), 32 , pp. 455-487, 2020, (Open Access).
In this paper, we provide a novel distributional solution framework to handle jumps and Dirac impulses on the boundaries of the domain of a hyperbolic PDE. It also includes a nice example of electrical power lines (modeled via the telegraph equation) with a switching transformer (modeled by a switched DAE). The simulations nicely show how a Dirac impulse (induced by a switch) is moving through time and space as predicted by the theory.