  We calculate the survival probability of an immobile target surrounded by a
sea of uncorrelated diffusive or subdiffusive evanescent traps, i.e., traps
that disappear in the course of their motion. Our calculation is based on a
fractional reaction-subdiffusion equation derived from a continuous time random
walk model of the system. Contrary to an earlier method valid only in one
dimension (d=1), the equation is applicable in any Euclidean dimension d and
elucidates the interplay between anomalous subdiffusive transport, the
irreversible evanescence reaction and the dimension in which both the traps and
the target are embedded. Explicit results for the survival probability of the
target are obtained for a density \rho(t) of traps which decays (i)
exponentially and (ii) as a power law. In the former case, the target has a
finite asymptotic survival probability in all integer dimensions, whereas in
the latter case there are several regimes where the values of the decay
exponent for \rho(t) and the anomalous diffusion exponent of the traps
determine whether or not the target has a chance of eternal survival in one,
two and three dimensions.
