INTERPLAY OF VISCOSITY AND DRY FRICTION IN RATE-INDEPENDENT EVOLUTIONS WITH NONCONVEX ENERGIES

Ricarda Rossi (Università di Brescia, Italy)

The approximation of rate-independent problems by viscosity regularization has recently attracted a good deal of attention, especially in connection with the problem of describing the system behaviour at jump points, in the case of a nonconvex driving energy functional.
In this talk, based on an ongoing collaboration with Alexander Mielke and Giuseppe Savare', we illustrate a technique for taking the vanishing viscosity limit, which is based on arc-length reparametrization. In this way, in the limit we obtain a novel formulation for rate-independent problems, which highlights the interplay of viscous and rate-independent effects in the jump regime.
Finally, we show how our results can be extended to a purely metric framewrok, in view of a greater flexibility in the applications to rate-independent problems.