  We study the dynamics of an interacting Bose-Hubbard chain coupled to a
non-Markovian environment. Our basic tool is the reduced generating functional
expressed as a path integral over spin-coherent states. We calculate the
leading contribution to the corresponding effective action, and by minimizing
it, we derive mean-field equations that can be numerically solved. With this
tool at hand, we examine the influence of the system's initial conditions and
interparticle interactions on the dissipative dynamics. Moreover, we
investigate the presence of memory effects due to the non-Markovian
environment.
