Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 02, pp. 1-20.

Title: Two-scale convergence of a model for flow in a partially fissured medium

Authors: G. W. Clark  (Virginia Commonwealth Univ., VA, USA)
         R. E. Showalter (Univ. of Texas at Austin, TX, USA)
         
Abstract: 
The distributed-microstructure model for the flow of single
phase fluid in a partially fissured composite medium due to
Douglas-Peszynska-Showalter [12] is extended to a
quasi-linear version. This model contains the geometry of the local
cells distributed throughout the medium, the flux exchange across
their intricate interface with the imbedded fissure system, and the
secondary flux resulting from diffusion paths within the matrix. Both
the exact but highly singular micro-model and the macro-model are
shown to be well-posed, and it is proved that the solution of the
micro-model is two-scale convergent to that of the macro-model as the
spatial parameter goes to zero. In the linear case, the effective
coefficients are obtained by a partial decoupling of the homogenized
system.


Submitted October 28, 1998. Published January 14, 1999.
Math Subject Classification: 35A15, 35B27, 76S05
Key Words: fissured medium; homogenization; two-scale convergence; 
           dual permeability; modeling; microstructure