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. For a particular choice of the initial data, we reach first- and second-order estimates. For general initial data, lower-order estimates are proven and their optimality is shown numerically.

翻译：我们考虑的是带有小参数 $\varepsilon>0$的受限制的双曲单方程,在限值中它会翻转抛物体,即,$\varepsilon=0美元。将讨论由此形成的系统的稳妥性,并将相应的解决方案按参数 $\varepsilon$进行比较。在分析中,我们将系统方程视为基于问题变式配方的局部差值。对于最初数据的特定选择,我们将得出第一和第二级估计数。对于一般初始数据,较低级估计数得到证明,其最佳性以数字表示。