  In a very long Gaussian polymer on time scales shorter that the maximal
relaxation time, the mean squared distance travelled by a tagged monomer grows
as ~t^{1/2}. We analyze such sub-diffusive behavior in the presence of one or
two absorbing boundaries and demonstrate the differences between this process
and the sub-diffusion described by the fractional Fokker-Planck equation. In
particular, we show that the mean absorption time of diffuser between two
absorbing boundaries is finite. Our results restrict the form of the effective
dispersion equation that may describe such sub-diffusive processes.
