Electron. J. Diff. Eqns.,
Vol. 1999(1999), No. 02, pp. 120.
Twoscale convergence of a model for flow in a partially fissured medium
G. W. Clark & R. E. Showalter
Abstract:
The distributedmicrostructure model for the flow of single
phase fluid in a partially fissured composite medium due to
DouglasPeszynskaShowalter [12] is extended to a
quasilinear 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 micromodel and the macromodel are
shown to be wellposed, and it is proved that the solution of the
micromodel is twoscale convergent to that of the macromodel 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, twoscale convergence,
dual permeability, modeling, microstructure
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G. W. Clark
Department of Mathematical Sciences,
Virginia Commonwealth University
Richmond, VA 23284 USA
email: gwclark@saturn.vcu.edu 

Ralph E. Showalter
Department of Mathematics,
University of Texas at Austin
Austin, TX 78712 USA
email: show@math.utexas.edu 
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