Multiscale analysis of singularly perturbed finite dimensional gradient flows: the minimizing movement approach

We perform a multiscale analysis of  the asymptotics of finite dimensional singularly perturbed gradient flows by solving a discrete-in-time minimization scheme. When the ratio between the viscosity parameter and the time scale diverges, we rigorously prove the convergence to a Balanced Viscosity solution of the stationary problem. We also characterize the limit evolution corresponding to an asymptotically finite ratio between the scales, describing the behaviour at the jumps by means of a discrete crease energy.
This is a joint work with Giovanni Scilla (Università di Napoli Federico II).

Contact person: Giacomo Albi