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- W4300786502 abstract "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 $mu$. 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 $mudownarrow 0$ and $muuparrow infty$. We shall prove convergence to Energetic solutions in the former case, and to Balanced Viscosity solutions in the latter situation." @default.
- W4300786502 created "2022-10-04" @default.
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- W4300786502 date "2017-02-01" @default.
- W4300786502 modified "2023-09-23" @default.
- W4300786502 title "From Visco-Energetic to Energetic and Balanced Viscosity solutions of rate-independent systems" @default.
- W4300786502 doi "https://doi.org/10.48550/arxiv.1702.00136" @default.
- W4300786502 hasPublicationYear "2017" @default.
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