  In this paper, in the setting of Hilbert spaces, we consider a Tikhonov
regularized second-order plus first-order primal-dual dynamical system with
asymptotically vanishing damping for a linear equality constrained convex
optimization problem. The convergence properties of the proposed dynamical
system depend heavily upon the choice of the Tikhonov regularization parameter.
When the Tikhonov regularization parameter decreases rapidly to zero, we
establish the fast convergence rates of the primal-dual gap, the objective
function error, the feasibility measure, and the gradient norm of the objective
function along the trajectory generated by the system. When the Tikhonov
regularization parameter tends slowly to zero, we prove that the primal
trajectory of the Tikhonov regularized dynamical system converges strongly to
the minimal norm solution of the linear equality constrained convex
optimization problem. Numerical experiments are performed to illustrate the
efficiency of our approach.
