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.

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

MIELKE, ALEXANDER;ROSSI, RICCARDA;SAVARE', GIUSEPPE
2016-01-01

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1178297
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