Abstract
We consider a compressible viscous flow in a bounded porous domain which consists of two parts: A system G1 of fractures antl a system G2 of porous blocks. It is assumed that the blocks G2 have a low permeability and the main flow occurs through G1 whereas the bulk porosity of G1 is very small cotnparetl to the one of G2. The material laws relating pressures and densities are supposed to be single-valued (i.e. the local pressure defines the local density and vice versa) but unbountletl thus allowing for power- and exponential laws, e.g. Following the idea of “Two-Compartment” models, separate pressure pi (i = l , 2 ) for the flow in the two compartments and G1 and G2Gare introduced. The resulting (possibly) highly nonlinear equations are shown to be well-posed in appropriate Hölder spares. As a by-product one obtains the convergence of a reiteration scheme as well as some sort of a maximum principle for the resulting pseudo-parabolic initial boundary value problem.