Asymptotic behaviour of fast diffusions on graphs

Abstract

We investigate fast diffusions on finite directed graphs. We prove results in a way dual to presented in Bobrowski, A. Ann. Henri Poincaré (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.

24 pages, 1 figure