  We investigate the existence and uniqueness of (locally) absolutely
continuous trajectories of a penalty term-based dynamical system associated to
a constrained variational inequality expressed as a monotone inclusion problem.
Relying on Lyapunov analysis and on the ergodic continuous version of the
celebrated Opial Lemma we prove weak ergodic convergence of the orbits to a
solution of the constrained variational inequality under investigation. If one
of the operators involved satisfies stronger monotonicity properties, then
strong convergence of the trajectories can be shown.
