  We address the minimization of the sum of a proper, convex and lower
semicontinuous with a (possibly nonconvex) smooth function from the perspective
of an implicit dynamical system of forward-backward type. The latter is
formulated by means of the gradient of the smooth function and of the proximal
point operator of the nonsmooth one. The trajectory generated by the dynamical
system is proved to asymptotically converge to a critical point of the
objective, provided a regularization of the latter satisfies the
Kurdyka-\L{}ojasiewicz property. Convergence rates for the trajectory in terms
of the \L{}ojasiewicz exponent of the regularized objective function are also
provided.
