  In this note we study the singular vanishing-viscosity limit of a gradient
flow set in a finite-dimensional Hilbert space and driven by a smooth, but
possibly non convex, time-dependent energy functional. We resort to ideas and
techniques from the variational approach to gradient flows and rate-independent
evolution to show that, under suitable assumptions, the solutions to the
singularly perturbed problem converge to a curve of stationary points of the
energy, whose behavior at jump points is characterized in terms of the notion
of Dissipative Viscosity solution. We also provide sufficient conditions under
which Dissipative Viscosity solutions enjoy better properties, which turn them
into Balanced Viscosity solutions. Finally, we discuss the generic character of
our assumptions.
