R. Showalter
UT Austin
Deformable Composite Porous Media
We discuss a variety of models of deformation and flow in composite
porous media. Classical examples of parallel type are briefly
recalled, and then distributed microstructure models are discussed.
Existence, uniqueness and regularity theory will be described for
initial-boundary-value problems for the systems of partial
differential equations which describe these models of diffusion and
deformation in composite porous media. The systems are resolved as
linear degenerate evolution equations in Hilbert space, and modeling
issues will be discussed.
Department of Mathematics,
The University of Texas at Austin,
Austin, TX 78712
Department of Mathematics,
The University of Texas at Austin,
Austin, TX 78712
show@math.utexas.edu
Key words and phrases: Biot consolidation problem, poro-elasticity, deformable
porous media, coupled quasi-static, secondary consolidation,
degenerate evolution equations, initial-boundary-value problems,
existence-uniqueness theory, regularity, homogenization
1991 Mathematics Subject Classification: 35D05, 35D10, 35K50, 35K65, 73C35, 76S05
