Microstructure Diffusion Models with Secondary Flux

Totally fissured media in which the cells are isolated by the fissure system are effectively described by double porosity models with microstructure. These models contain the geometry of the individual cells or pores in the medium and the flux across their interface with the fissures which surrounds them. We extend these models to include the case of partially fissured media in which a secondary flux effect arises from cell-to-cell diffusion paths. These quasilinear problems are formulated in appropriate spaces for which the cells respond to the local linearization of the fissure pressure. It is shown that they are well-posed and that the solutions depend continuously on parameters that determine the models.