  We study the dynamical evolution of a stellar disk orbiting a massive black
hole. We explore the role of two-body relaxation, mass segregation, stellar
evolution and binary heating in affecting the disk evolution, and consider the
impact of the nuclear cluster structure and the stellar-disk mass-function. We
use analytic arguments and numerical calculations, and apply them to study the
evolution of a stellar disk (similar to that observed in the Galactic center;
GC), both on the short (few Myr) and longer (100 Myr) evolutionary timescales.
We find the dominant processes affecting the disk evolution are two-body
relaxation and mass segregation where as binary heating have only a little
contribution. Massive stars play a dominant role in kinematically heating low
mass stars, and driving them to high eccentricities/inclinations. Multi-mass
models with realistic mass-functions for the disk stars show the disk structure
to be mass stratified, with the most massive stars residing in thinner
structures. Stellar evolution plays an important role in decreasing the number
of massive stars with time, thereby leading to slower relaxation, where the
remnant compact objects of these stars are excited to higher
eccentricities/inclinations. At these later evolutionary stages dynamical
heating by the nuclear cluster plays a progressively more important role. We
conclude that the high eccentricities of the disk-stars in the Galactic Center
suggest that the disk formed with initially high eccentricities, or that
collective or secular processes dominate the disk evolution. Finally, we find
that the disk structure is expected to keep a thin structure even after 100
Myrs. It therefore suggests earlier disks now containing only older, lower mass
stars might still be observed in the Galactic center, unless destroyed/smeared
by other non-two-body relaxation processes.
