We consider the long-term evolution of gaseous disks fed by the vaporization of small particles produced in a collisional cascade inside the Roche limit of a 0.6 white dwarf. Adding solids with radius at a constant rate into a narrow annulus leads to two distinct types of evolution. When , the cascade generates a fairly steady accretion disk where the mass transfer rate of gas onto the white dwarf is roughly and the mass in gas is g, where T0 is the temperature of the gas near the Roche limit and is the dimensionless viscosity parameter. If , the system alternates between high states with large mass transfer rates and low states with negligible accretion. Although either mode of evolution adds significant amounts of metals to the white dwarf photosphere, none of our calculations yield a vertically thin ensemble of solids inside the Roche limit. X-ray observations can place limits on the mass transfer rate and test this model for metallic line white dwarfs.