Asymptotic behaviour of fast diffusions on graphs

2019/01/07 by Adam Gregosiewicz, Gregosiewicz, Adam
Mathematics · #35B40 (Secondary) #47D06 (Primary) #47D07 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:47D06 #msc:47D07

paper · pdf · doi:10.48550/arxiv.1901.02072

24 pages, 1 figure

arxiv created 2019/02/19 · arxiv updated 2019/02/20

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 L¹ and L² as the diffusions' speed increases and the probability of a particle passing through a vertex decreases.

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