We begin with the initial-boundary-value problem for a coupled system of partial differential equations which describes the Biot consolidation model in poro-elasticity. Existence, uniqueness and regularity theory is developed for the quasi-static case as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system. Current work on the theoretical foundations of this model and appropriate extensions to models with elastic-viscous-plastic media or nonhomogeneous media will be briefly described.

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1999-2000 Reactive Flow and Transport Phenomena