From the mathematical point of view, the mixed-type systems (first order in time, second order in space) that we have considered in the previous chapter are associated with the parabolic type of equations. The prototype could be the Navier–Stokes equation of fluid dynamics, where second-order space derivatives appear in the viscosity terms. Parabolic equations are not the ones usually associated with causal propagation phenomena, where a finite propagation speed can be derived in a natural way from the governing equations.
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Bona, C., Bona-Casas, C., Palenzuela-Luque, C. (2009). First-Order Hyperbolic Systems. In: Elements of Numerical Relativity and Relativistic Hydrodynamics. Lecture Notes in Physics, vol 783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01164-1_4
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