  In order to solve the minimization of a nonsmooth convex function, we design
an inertial second-order dynamic algorithm, which is obtained by approximating
the nonsmooth function by a class of smooth functions. By studying the
asymptotic behavior of the dynamic algorithm, we prove that each trajectory of
it weakly converges to an optimal solution under some appropriate conditions on
the smoothing parameters, and the convergence rate of the objective function
values is o(t^-2). We also show that the algorithm is stable, that is, this
dynamic algorithm with a perturbation term owns the same convergence properties
when the perturbation term satisfies certain conditions. Finally, we verify the
theoretical results by some numerical experiments.
