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.