Singular perturbation results for linear partial differential-algebraic equations of hyperbolic type

We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed and the corresponding solutions are compared in terms of the parameter $\varepsilon$. For the analysis, we consider the system equations as partial differential-algebraic equation based on the variational formulation of the problem. Depending on the particular choice of the initial data, we reach first- and second-order estimates. Optimality of the lower-order estimates for general initial data is shown numerically.