We consider the well-known minimizing-movement approach to the definition of a solution of gradient-flow type equations by means of an implicit Euler scheme depending on an energy and a dissipation term. We perturb the energy by considering a ($ \Gamma $-converging) sequence and the dissipation by varying multiplicative terms. The scheme depends on two small parameters $ \varepsilon $ and $ \tau $, governing energy and time scales, respectively. We characterize the extreme cases when $ \varepsilon/\tau $ and $ \tau/ \varepsilon $ converges to $ 0 $ sufficiently fast, and exhibit a sufficient condition that guarantees that the limit is indeed independent of $ \varepsilon $ and $ \tau $. We give examples showing that this in general is not the case, and apply this approach to study some discrete approximations, the homogenization of wiggly energies and geometric crystalline flows obtained as limits of ferromagnetic energies.

中文翻译：

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扰动最小化功能族的运动

我们考虑一种众所周知的最小化运动方法，该方法通过依赖能量和耗散项的隐式欧拉方案来定义梯度流类型方程的解。我们通过考虑一个（$ \ Gamma $ -converging）序列来扰动能量，并通过改变乘法项来耗散能量。该方案取决于分别控制能量和时间尺度的两个小参数$ \ varepsilon $和$ \ tau $。我们描述了$ \ varepsilon / \ tau $和$ \ tau / \ varepsilon $足够快地收敛到$ 0 $的极端情况，并展示了一个足以保证极限确实独立于$ \ varepsilon $和$ \的条件。 tau $。我们提供的示例表明，通常情况并非如此，并应用此方法研究了一些离散近似值，