We investigate fast diffusions on finite directed graphs. We prove results in a way dual to presented in Bobrowski, A. Ann. Henri Poincar\'e (2012) 13(6): 1501-1510 and Bobrowski, A., Morawska, K. DCDS-B (2012), 17(7): 2313-2327, and obtain asymptotic behaviour of a diffusion semigroup on a graph in $ L^1 $ and $ L^2 $ as the diffusions' speed increases and the probability of a particle passing through a vertex decreases.

中文翻译：

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图上快速扩散的渐近行为

我们研究了有限有向图上的快速扩散。我们以与 Bobrowski, A. Ann 中呈现的双重方式证明结果。Henri Poincar\'e (2012) 13(6): 1501-1510 和 Bobrowski, A., Morawska, K. DCDS-B (2012), 17(7): 2313-2327，并获得扩散半群的渐近行为在 $ L^1 $ 和 $ L^2 $ 的图上，随着扩散速度的增加和粒子通过顶点的概率降低。