This paper focuses on weak solvability concepts for rate-independent systems in a metric setting. Visco-Energetic solutions have been recently obtained by passing to the time-continuous limit in a time-incremental scheme, akin to that for Energetic solutions, but perturbed by a ‘viscous’ correction term, as in the case of Balanced Viscosity solutions. However, for Visco-Energetic solutions this viscous correction is tuned by a fixed parameter μ. The resulting solution notion is characterized by a stability condition and an energy balance analogous to those for Energetic solutions, but, in addition, it provides a fine description of the system behavior at jumps as Balanced Viscosity solutions do. Visco-Energetic evolution can be thus thought as ‘in-between’ Energetic and Balanced Viscosity evolution. Here we aim to formalize this intermediate character of Visco-Energetic solutions by studying their singular limits as μ ↓ 0 and μ ↑∞. We shall prove convergence to Energetic solutions in the former case, and to Balanced Viscosity solutions in the latter situation.
CITATION STYLE
Rossi, R., & Savaré, G. (2017). From visco-energetic to energetic and balanced viscosity solutions of rate-independent systems. In Springer INdAM Series (Vol. 22, pp. 489–531). Springer International Publishing. https://doi.org/10.1007/978-3-319-64489-9_19
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