<p style='text-indent:20px;'>In this paper, we derive the mean-field limit of a collective dynamics model with time-varying weights, for weight dynamics that preserve the total mass of the system as well as indistinguishability of the agents. The limit equation is a transport equation with source, where the (non-local) transport term corresponds to the position dynamics, and the (non-local) source term comes from the weight redistribution among the agents. We show existence and uniqueness of the solution for both microscopic and macroscopic models and introduce a new empirical measure taking into account the weights. We obtain the convergence of the microscopic model to the macroscopic one by showing continuity of the macroscopic solution with respect to the initial data, in the Wasserstein and Bounded Lipschitz topologies.</p>

中文翻译：

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具有时变权重的集体动力学的平均场极限

<p style='text-indent:20px;'>在本文中，我们推导了具有时变权重的集体动力学模型的平均场极限，用于保持系统总质量和不可区分性的权重动力学的代理。极限方程是一个有源的传输方程，其中（非局部）传输项对应于位置动态，（非局部）源项来自代理之间的权重再分配。我们展示了微观和宏观模型解决方案的存在性和唯一性，并引入了一种考虑权重的新经验度量。在 Wasserstein 和有界 Lipschitz 拓扑中，我们通过显示宏观解相对于初始数据的连续性来获得微观模型与宏观模型的收敛性。</p>