The slow diffusion limit for the survival probability in reactive diffusion equations

We consider the Smoluchowski equation with a coordinate-dependent reactivity and obtain asymptotic expansions for the survival probability and the mean lifetime as power series in the diffusion constant. The coefficients in this expansion may depend on both temporal and spatial variables. Using the present results together with the previously derived expansion for the fast diffusion limit, we are able to obtain useful Padé approximations for the dependence of the mean lifetime on the diffusion coefficient.