  Large deviations principles characterize the exponential decay rates of the
probabilities of rare events. Cerrai and Rockner [13] proved that systems of
stochastic reaction-diffusion equations satisfy a large deviations principle
that is uniform over bounded sets of initial data.
  This paper proves uniform large deviations results for a system of stochastic
reaction--diffusion equations in a more general setting than Cerrai and
Rockner. Furthermore, this paper identifies two common situations where the
large deviations principle is uniform over unbounded sets of initial data,
enabling the characterization of Freidlin-Wentzell exit time and exit shape
asymptotics from unbounded sets.
