  We investigate the asymptotic properties of the trajectories generated by a
second-order dynamical system with Hessian driven damping and a Tikhonov
regularization term in connection with the minimization of a smooth convex
function in Hilbert spaces. We obtain fast convergence results for the function
values along the trajectories. The Tikhonov regularization term enables the
derivation of strong convergence results of the trajectory to the minimizer of
the objective function of minimum norm.
