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.
Keywords
Cite
@article{arxiv.1309.6291,
title = {Balanced Viscosity (BV) solutions to infinite-dimensional rate-independent systems},
author = {Alexander Mielke and Riccarda Rossi and Giuseppe Savaré},
journal= {arXiv preprint arXiv:1309.6291},
year = {2018}
}