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”:
Borsche, Raul; Kocoglu, Damla; Trenn, Stephan A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs Unpublished 2020, (submitted for publication). Abstract | Links | BibTeX @unpublished{BorsKoco20pp,
title = {A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs},
author = {Raul Borsche and Damla Kocoglu and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2020/07/Preprint-BKT200707.pdf, Preprint
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5884, Preprint (on TU-KL server)},
year = {2020},
date = {2020-07-07},
abstract = {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.},
note = {submitted for publication},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
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. |
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.
