We report on some recent progress in the mathematical
theory of nonlinear fluid transport and poro-mechanics, specifically,
the design, analysis and application of mathematical models for the
flow of fluids driven by the coupled pressure and stress
distributions within a deforming heterogeneous porous structure.
The goal of this work is to develop a set of mathematical models of
coupled flow and deformation processes as a basis for fundamental
research on the theoretical and numerical modeling and simulation of
flow in deforming heterogeneous porous media.