The present work is a study of three degenerate, linear parabolic
systems of equations, each of which represents a version of the so-called
double porosity model for underground fluid flows in natural fractured
rock. These systems of equations together with initial and boundary
conditions describe single-phase flows in fluids, slightly compressible,
in large confined homogeneous reservoirs under general conditions
including those of typical well tests. Analytic solutions are given as
convolutions of initial and source data with fundamental solutions for
each system. We establish that the problems are well-posed for all
initial conditions likely to arise in practice. We obtain, using the
theory of generalized functions, classes of all functions in which
solutions exist, are unique and depend continuously on the initial data
for appropriate restrictions. We consider two of the models to be the
main versions relevant for flows in natural fractured rock, including
typical basalt formations. They apply to short-time flows on order of
the duration of typical pressure transient tests, and they are
potentially useful for obtaining accurate values of formation parameters
from well test data. We also show that the inverse problems of estimating parameters from well data are well-posed, i.e., that parameter
values obtained are unique and depend continuously on the data
