Distributed Microstructure Models of Porous Media
Ralph E. Showalter · Birkhäuser Basel eBooks · 1993
Laminar flow through fissured or otherwise highly inhomogeneous media leads to very singular initial-boundary-value problems for equations with rapidly oscillating coefficients. The limiting case (by homogenization) is a continuous distribution of model cells which represent a valid approximation of the finite (singular) case, and we survey some recent results on the theory of such systems. This is developed as an application of continuous direct sums of Banach spaces which arise rather naturally as the energy or state spaces for the corresponding (stationary) variational or (temporal) dynamic problems. We discuss the basic models for a totally fissured medium, the extension to include secondary flux in partially fissured media, and the classical model systems which are realized as limiting cases of the microstructure models. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.