Abstract
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.
Highlights
We develop a rigorous solution theory for systems where a linear hyperbolic partial differential equation (PDE) is coupled with a switched differentialalgebraic equation (DAE) via boundary conditions (BC), see Fig. 1 as an overview
The output of the switched DAE provides the boundary condition for the PDE and the boundary values of the PDE serve as input to the DAE
This is a wider class compared to the solutions of small bounded variation, e.g. used in [4] where a nonlinear hyperbolic PDE is coupled to an ODE
Summary
We develop a rigorous solution theory for systems where a linear hyperbolic partial differential equation (PDE) is coupled with a switched differentialalgebraic equation (DAE) via boundary conditions (BC), see Fig. 1 as an overview. Such systems occur, for example, when modelling power grids using the telegraph equation [8] including switches (e.g. induced by disconnecting lines), water flow. We illustrate the results by numerical simulations of the power grid example
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