Previous studies showed that the dynamic equations for a porous fluid-saturated solid may lose hyperbolicity and thus render the boundary-value problem ill-posed while the equations for the same but dry solid remain hyperbolic. This paper presents sufficient conditions for hyperbolicity in both dry and saturated states. Fluid-saturated solids are described by two different systems of equations depending on whether the permeability is zero or nonzero (locally undrained and drained conditions, respectively). The paper also introduces a notion of wave speed consistency between the two systems as a necessary condition which must be satisfied in order for the solution in the locally drained case to tend to the undrained solution as the permeability tends to zero. It is shown that the symmetry and positive definiteness of the acoustic tensor of the skeleton guarantee both hyperbolicity and the wave speed consistency of the equations.

先前的研究表明，多孔流体饱和固体的动力学方程可能会失去双曲性，从而使边值问题不适当地出现，而相同但干燥的固体的方程仍是双曲的。本文为干态和饱和态下的双曲提供了充分的条件。根据渗透率是零还是非零（分别是局部不排水和排水条件），通过两个不同的方程组来描述流体饱和的固体。本文还介绍了两个系统之间的波速一致性的概念，这是必须满足的必要条件，以使局部排水情况下的解决方案在渗透率趋于零时趋向于不排水解决方案。