  The subject of this article is a matched microstructure model for Newtonian
fluid flows in fractured porous media. This is a homogenized model which takes
the form of two coupled parabolic differential equations with boundary
conditions in a given (two-scale) domain in Euclidean space. The main objective
is to establish the local well-posedness in the strong sense of the flow. Two
main settings are investigated: semi-linear systems with linear boundary
conditions and semi-linear systems with nonlinear boundary conditions. With the
help of analytic semigoups we establish local well-posedness and investigate
the long-time behaviour of the solutions in the first case: we establish global
existence and show that solutions converge to zero at an exponential rate.
