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On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms

Mielke, A and Zelik, S (2014) On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 13 (1). pp. 67-135.

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Abstract

We consider semilinear and quasilinear parabolic systems with a nonsmooth rate-independent and a viscous dissipation term in the limit of very slow loading rates, or equivalently with fixed loading and vanishing viscosity " > 0. Because for nonconvex energies the solutions will develop jumps, we consider the vanishing-viscosity limit for the graphs of the solutions in the extended state space in arclength parametrization. Here the choice of the viscosity norm for parametrization is crucial to keep the subdifferential structure of the problem. A crucial point in the analysis are new a priori estimates that are rate independent and that allow us to show that the total length of the graph remains bounded in the vanishing-viscosity limit. To derive these estimates we combine parabolic regularity estimates with ideas from rate-independent systems.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Mielke, AUNSPECIFIEDUNSPECIFIED
Zelik, SUNSPECIFIEDUNSPECIFIED
Date : 1 January 2014
Identification Number : 10.2422/2036-2145.201004_003
Uncontrolled Keywords : Science & Technology, Physical Sciences, Mathematics, MATHEMATICS, NONLINEAR EVOLUTION-EQUATIONS, QUASI-STATIC EVOLUTION, LONG-TIME BEHAVIOR, WELL-POSEDNESS, ATTRACTORS, MODEL, PLASTICITY, GROWTH
Related URLs :
Additional Information : Copyright 2014 SCUOLA NORMALE SUPERIORE
Depositing User : Symplectic Elements
Date Deposited : 26 Aug 2015 17:47
Last Modified : 26 Aug 2015 17:47
URI: http://epubs.surrey.ac.uk/id/eprint/806828

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