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Title: Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems
Authors: Mielke, AlexanderRossi, RiccardaSavaré, Giuseppe
URI: https://doi.org/10.34657/2042
https://oa.tib.eu/renate/handle/123456789/3218
Issue Date: 2013
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1845, ISSN 0946 – 8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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: Doubly nonlinear equations; generalized gradient flows; rate-independent systems; vanishing-viscosity limit; variational Gamma convergence; energy-dissipation balance; arclength parameterized solutions; Nichtlineare Evolutionsgleichung
Type: report; Text
Publishing status: publishedVersion
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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Mielke, Alexander, Riccarda Rossi and Giuseppe Savaré, 2013. Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Mielke, A., Rossi, R. and Savaré, G. (2013) Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Mielke A, Rossi R, Savaré G. Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik; 2013.
Mielke, A., Rossi, R., & Savaré, G. (2013). Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems (Version publishedVersion). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Mielke A, Rossi R, Savaré G. Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik; 2013.


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