Index concepts for linear mixed systems of differential-algebraic and hyperbolic-type equations

For many technical systems, the use of a refined network modeling approach leads to hyperbolic-type initial-boundary value problems of partial differe ntial-algebraic equations ( PDAEs). The boundary conditions of these system s are governed by time-dependent differential-algebraic equations (DAEs) th at couple the PDAE system with the network elements that are modeled by DAE s in time only. In order to classify these systems, we extend some index no tions that have already been introduced to treat parabolic-type problems. A perturbation index is considered that reflects the sensitivity of the mixe d system to slight perturbations in the right-hand side of the PDAEs, as we ll as in the input signals of the DAE systems and initial values. In order to make an a posteriori analysis of semidiscretization in space and time, w e introduce additionally a space and a method of lines (MOL) index. Here on e is especially interested in whether the semidiscretized systems properly re ect the properties of the underlying systems. We will show that these in dices may detect an artificial sensitivity with respect to perturbations, e .g., if the semidiscretization does not consider the information transport along the characteristics.