Abstract In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely monotonic we obtain a drastically simplified condition which ensures boundedness of the associates semigroup. If the characteristic function satisfies certain additional conditions we deduce sharp rates of convergence to equilibrium. We moreover address the important and delicate issue of the role of the infinite system in understanding the asymptotic behaviour of large but finite systems, and we provide a precise way of obtaining size-independent rates of convergence for families of finite-dimensional systems. Finally, we illustrate our abstract results in the setting of the well-known platoon problem.

中文翻译：

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大型常微分方程组的渐近和逼近

摘要 在本文中，我们继续早期对耦合微分方程无限系统的渐近行为的研究。在我们系统的所谓特征函数完全单调的温和假设下，我们获得了一个大大简化的条件，它确保了关联半群的有界性。如果特征函数满足某些附加条件，我们将推导出收敛到均衡的急剧速率。此外，我们还解决了无限系统在理解大型但有限系统的渐近行为方面的作用的重要而微妙的问题，并且我们提供了一种精确的方法来获得有限维系统族的大小无关收敛速度。最后，我们在众所周知的排问题的设置中说明了我们的抽象结果。