Electron. J. Diff. Eqns., Vol. 1999(1999), No. 02, pp. 1-20.

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

G. W. Clark & R. E. Showalter

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

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  G. W. Clark
Department of Mathematical Sciences, Virginia Commonwealth University
Richmond, VA 23284 USA
e-mail: gwclark@saturn.vcu.edu
Ralph E. Showalter
Department of Mathematics, University of Texas at Austin
Austin, TX 78712 USA
e-mail: show@math.utexas.edu

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