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DCDS-B

The formulation and existence theory is presented for a system modeling
diffusion of a slightly compressible fluid through a partially saturated poroelastic
medium. Nonlinear effects of density, saturation, porosity and permeability
variations with pressure are included, and the seepage surface is determined by a
variational inequality on the boundary.

DCDS

A two-scale microstructure model of current flow in a medium with
continuously distributed capacitance is extended to include
nonlinearities in the conductance across the interface between the local
capacitors and the global conducting medium.
The resulting degenerate system of partial differential equations is shown
to be in the form of a semilinear parabolic evolution equation in
Hilbert space. It is shown directly that such an equation is equivalent
to a subgradient flow and, hence, displays the appropriate parabolic
regularizing effects.
Various limiting cases are identified and the corresponding convergence
results obtained by letting selected parameters tend to
infinity.

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