This paper focuses on weak solvability concepts for rate-independent systemsin a metric setting. Visco-Energetic solutions have been recently obtained bypassing to the time-continuous limit in a time-incremental scheme, akin to thatfor Energetic solutions, but perturbed by a `viscous' correction term, as inthe case of Balanced Viscosity solutions. However, for Visco-Energeticsolutions this viscous correction is tuned by a fixed parameter $\mu$. Theresulting solution notion is characterized by a stability condition and anenergy balance analogous to those for Energetic solutions, but, in addition, itprovides a fine description of the system behavior at jumps as BalancedViscosity solutions do. Visco-Energetic evolution can be thus thought as`in-between' Energetic and Balanced Viscosity evolution. Here we aim toformalize this intermediate character of Visco-Energetic solutions by studyingtheir singular limits as $\mu\downarrow 0$ and $\mu\uparrow \infty$. We shallprove convergence to Energetic solutions in the former case, and to BalancedViscosity solutions in the latter situation.
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机译：本文着重于度量设置中与速率无关的系统的弱可解性概念。最近，在时间增量方案中绕过了时间连续极限而获得了Visco-Energytic解决方案，类似于Energytic解决方案，但是像平衡粘度解决方案一样，它受“粘性”校正项的干扰。但是，对于Visco-Energeticsolutions，此粘性校正是通过固定参数$ \ mu $进行调整的。结果解决方案的概念具有类似于能量解决方案的稳定条件和无能平衡的特征，但是，此外，它还提供了平衡粘度解决方案对系统行为的精确描述。粘滞能量演化因此可以被认为是“粘滞能量平衡”和“平衡粘稠度演化之间的”。在这里，我们旨在通过研究它们的奇异极限（$ \ mu \ downarrow 0 $和$ \ mu \ uparrow \ infty $）来规范化Visco-Energytic解决方案的中间特征。在前一种情况下，我们将证明对能量解决方案的收敛，在后一种情况下，我们将证明对平衡粘度的解决方案。
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