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Kocoglu, Damla; Trenn, Stephan A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs Unpublished 2019. Abstract | Links | BibTeX @unpublished{BorsKoco19pp,
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/2019/12/Preprint-BKT191128.pdf},
year = {2019},
date = {2019-11-28},
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.},
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tppubtype = {unpublished}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.
