  In the papers (Shvidler, 1985 and 1993, and Shvidler and Karasaki, 1999,
2001, 2005, and 2008) we developed an approach for finding the exactly averaged
equations of flow and transport in porous media. We studied for steady state
flow with sources and also analyzed unsteady flow and nonreactive solute
transport in unbounded domains with stochastically homogeneous conductivity
random fields. In the base of the approach is the existence of appropriate
random Green's functions and relevant linear random operators. Examination of
random fields with global symmetry makes it possible to describe some different
types of averaged equations with non-local unique vector or tensor operators.
In this paper we substantially extend the approach and study more general
processes in bounded or unbounded fields of any dimensions and examine the
cases where the random fields of conductivity and porosity are stochastically
homogeneous or non-homogeneous.
