  Recent infrared observations have revealed presence of compact (radii <
R_Sun) debris disks around more than a dozen of metal-rich white dwarfs (WD),
likely produced by tidal disruption of asteroids. Accretion of high-Z material
from these disks may account for the metal contamination of these WDs. It was
previously shown using local calculations that the Poynting-Robertson (PR) drag
acting on the dense, optically thick disk naturally drives metal accretion onto
the WD at the typical rate \dot M_{PR} \approx 10^8 g/s. Here we extend this
local analysis by exploring global evolution of the debris disk under the
action of the PR drag for a variety of assumptions about the disk properties.
We find that massive disks (mass > 10^{20} g), which are optically thick to
incident stellar radiation inevitably give rise to metal accretion at rates
\dot M > 0.2\dot M_{PR}. The magnitude of \dot M and its time evolution are
determined predominantly by the initial pattern of the radial distribution of
the debris (i.e. ring-like vs. disk-like) but not by the total mass of the
disk. The latter determines only the disk lifetime, which can be several Myr or
longer. Evolution of an optically thick disk generically results in the
development of a sharp outer edge of the disk. We also find that the low mass
(< 10^{20} g), optically thin disks exhibit \dot M << \dot M_{PR} and evolve on
characteristic timescale \sim 10^5-10^6 yr, independent of their total mass.
