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

Tikhonov regularization of a second order dynamical system with Hessian driven damping