  This paper explores the effects of FUV radiation fields from external stars
on circumstellar disk evolution. Disks residing in young clusters can be
exposed to extreme levels of FUV flux from nearby OB stars, and observations
show that disks in such environments are being actively photoevaporated.
Typical FUV flux levels can be factors of \sim 10^{2} - 10^{4} higher than the
interstellar value. These fields are effective in driving mass loss from
circumstellar disks because they act at large radial distance from the host
star, i.e., where most of the disk mass is located, and where the gravitational
potential well is shallow. We combine viscous evolution (an \alpha-disk model)
with an existing FUV photoevaporation model to derive constraints on disk
lifetimes, and to determine disk properties as functions of time, including
mass loss rates, disk masses, and radii. We also consider the effects of X-ray
photoevaporation from the host star using an existing model, and show that for
disks around solar-mass stars, externally-generated FUV fields are often the
dominant mechanism in depleting disk material. For sufficiently large
viscosities, FUV fields can efficiently photoevaporate disks over the entire
range of parameter space. Disks with viscosity parameter \alpha = 10^{-3} are
effectively dispersed within 1-3 Myr; for higher viscosities (\alpha = 10^{-2})
disks are dispersed within \sim 0.25 - 0.5 Myr. Furthermore, disk radii are
truncated to less than \sim100 AU, which can possibly affect the formation of
planets. Our model predictions are consistent with the range of observed masses
and radii of proplyds in the Orion Nebula Cluster.
