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arXiv · 1710.05339

Generation via variational convergence of Balanced Viscosity solutions to rate-independent systems

Giovanni A. Bonaschi·Riccarda Rossi
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Abstract

In this paper we investigate the origin of the Balanced Viscosity solution concept for rate-independent evolution in the setting of a finite-dimensional space. Namely, given a family of dissipation potentials $(\Psi_n)_n$ with superlinear growth at infinity and a smooth energy functional $\mathcal{E}$, we enucleate sufficient conditions on them ensuring that the associated gradient systems $(\Psi_n,\mathcal{E})$ Evolutionary Gamma-converge to a limiting rate-independent system, understood in the sense of Balanced Viscosity solutions. In particular, our analysis encompasses both the vanishing-viscosity approximation of rate-independent systems and their stochastic derivation.

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Giovanni A. Bonaschi, Riccarda Rossi. 2017-10-15. Generation via variational convergence of Balanced Viscosity solutions to rate-independent systems. https://arxiv.org/abs/1710.05339

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