Balanced Viscosity (BV) solutions to infinite-dimensional rate-independent systems

Abstract

Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by adding a superlinear vanishing-viscosity dissipation.

We address the main issue of proving the existence of such limits for infinite-dimensional systems and of characterizing them by a couple of variational properties that combine a local stability condition and a balanced energy-dissipation identity.

A careful description of the jump behavior of the solutions, of their differentiability properties, and of their equivalent representation by time rescaling is also presented.

Our techniques rely on a suitable chain-rule inequality for functions of bounded variation in Banach spaces, on refined lower-semicontinuity compactness arguments, and on new BV-estimates that are of independent interest.