Calculus of Variations and Geometric Measure Theory

A. Mielke - R. Rossi - G. Savaré

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

created by rossi on 23 Sep 2013


Submitted Paper

Inserted: 23 sep 2013
Last Updated: 23 sep 2013

Year: 2013


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.