Singular perturbation results for linear partial differential-algebraic equations of hyperbolic type
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We consider constrained partial differential equations of hyperbolic type with a small parameter ε>0, which turn parabolic in the limit case, i.e., for ε=0. The well-posedness of the resulting systems is discussed and the corresponding solutions are compared in terms of the parameter ε. 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.
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