  We construct a protostellar disk model that takes into account the combined
effect of viscous evolution, photoevaporation and the differential radial
motion of dust grains and gas. For T Tauri disks, the lifetimes of dust disks
that are mainly composed of millimeter sized grains are always shorter than the
gas disks' lifetimes, and become similar only when the grains are fluffy
(density < 0.1 g cm^{-3}). If grain growth during the classical T Tauri phase
produces plenty of millimeter sized grains, such grains completely accrete onto
the star in 10^7 yr, before photoevaporation begins to drain the inner gas disk
and the star evolves to the weak line T Tauri phase. In the weak line phase,
only dust-poor gas disks remain at large radii (> 10 AU), without strong signs
of gas accretion nor of millimeter thermal emission from the dust. For Herbig
AeBe stars, the strong photoevaporation clears the inner disks in 10^6 yr,
before the dust grains in the outer disk migrate to the inner region. In this
case, the grains left behind in the outer gas disk accumulate at the disk inner
edge (at 10-100 AU from the star). The dust grains remain there even after the
entire gas disk has been photoevaporated, and form a gas-poor dust ring similar
to that observed around HR 4796A. Hence, depending on the strength of the
stellar ionizing flux, our model predicts opposite types of products around
young stars. For low mass stars with a low photoevaporation rate, dust-poor gas
disks with an inner hole would form, whereas for high mass stars with a high
photoevaporation rate, gas-poor dust rings would form. This prediction should
be examined by observations of gas and dust around weak line T Tauri stars and
evolved Herbig AeBe stars.
