3-dimensional physically consistent diffusion in anisotropic media with memory (Q1287012)

Summary: Some data on the flow of fluids exhibit properties which may not be interpreted with the classical theory of propagation of pressure and with the theory of fluids based on the classical Darcy law which states that the flux is proportional to the pressure gradient. In order to obtain a better representation of the flow and of the pressure of fluids, the Darcy law is here modified by introducing a memory formalism operating on the flow as well as on the pressure gradient, which implies a filtering of the pressure gradient without singularities; the properties of the filtering are also described. We also modify the second constitutive equation of diffusion, which relates the density variations of the fluid to its pressure variations, by introducing the rheology of the fluid represented by derivatives of fractional order. Moreover, we are able to consider anisotropic media. We derive a diffusion equation for anisotropic media, and find Green function for a point source.