Diffusion in Deformable Media

We begin with the initial-boundary-value problem for a coupled system of partial differential equations which describes the Biot consolidation model in poroelasticity. 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 foundations of the model and appropriate extensions to models with elasticviscous-plastic media or nonhomogeneous media will be briefly described.