Diffusion in Poro-Elastic Media

Existence, uniqueness, and regularity theory is developed for a general initialboundary- value problem for a system of partial differential equations which describes the Biot consolidation model in poro-elasticity as well as a coupled quasi-static problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasi-static system is resolved 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.