  We study the single-species diffusion-annihilation process with a
time-dependent reaction rate, lambda(t)=lambda_0 t^-omega. Scaling arguments
show that there is a critical value of the decay exponent omega_c(d) separating
a reaction-limited regime for omega > omega_c from a diffusion-limited regime
for omega < omega_c. The particle density displays a mean-field,
omega-dependent, decay when the process is reaction limited whereas it behaves
as for a constant reaction rate when the process is diffusion limited. These
results are confirmed by Monte Carlo simulations. They allow us to discuss the
scaling behaviour of coupled diffusion-annihilation processes in terms of
effective time-dependent reaction rates.
