WIAS Preprint No. 2902, (2021)

Balanced-Viscosity solutions to infinite-dimensional multi-rate systems


  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Rossi, Riccarda
    ORCID: 0000-0002-7808-0261

2020 Mathematics Subject Classification

  • 35Q74 47J30 49J40 49J45 49J52 74D10 74R99


  • Balanced-Viscosity solution, reparametrized solutions, energy-dissipation principle, generalized gradient systems, delamination model




We consider generalized gradient systems with rate-independent and rate-dependent dissipation potentials. We provide a general framework for performing a vanishing-viscosity limit leading to the notion of parametrized and true Balanced-Viscosity solutions that include a precise description of the jump behavior developing in this limit. Distinguishing an elastic variable $u$ having a viscous damping with relaxation time $eps^alpha$ and an internal variable $z$ with relaxation time $eps$ we obtain different limits for the three cases $alpha in (0,1)$, $alpha=1$ and $alpha>1$. An application to a delamination problem shows that the theory is general enough to treat nontrivial models in continuum mechanics.

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