Balanced Viscosity (BV) solutions to infinite-dimensional rate-independent systems
Alexander Mielke
Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, GermanyRiccarda Rossi
Università degli Studi di Brescia, ItalyGiuseppe Savaré
Università di Pavia, Italy
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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.
Cite this article
Alexander Mielke, Riccarda Rossi, Giuseppe Savaré, Balanced Viscosity (BV) solutions to infinite-dimensional rate-independent systems. J. Eur. Math. Soc. 18 (2016), no. 9, pp. 2107–2165
DOI 10.4171/JEMS/639