  In this paper, we explicitly calculate the quasi-potentials for the damped
semilinear stochastic wave equation when the system is of gradient type. We
show that in this case the infimum of the quasi-potential with respect to all
possible velocities does not depend on the density of the mass and does
coincide with the quasi-potential of the corresponding stochastic heat equation
that one obtains from the zero mass limit. This shows in particular that the
Smoluchowski-Kramers approximation can be used to approximate long time
behavior in the zero noise limit, such as exit time and exit place from a basin
of attraction.
