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Asymptotic behaviour of fast diffusions on graphs.

Authors :
Gregosiewicz, Adam
Source :
Semigroup Forum. 2020, Vol. 101 Issue 3, p619-653. 35p.
Publication Year :
2020

Abstract

We study a diffusion process on a finite graph with semipermeable membranes on vertices. We prove, in L 1 and L 2 -type spaces that for a large class of boundary conditions, describing communication between the edges of the graph, the process is governed by a strongly continuous semigroup of operators, and we describe asymptotic behaviour of the diffusion semigroup as the diffusions' speed increases at the same rate as the membranes' permeability decreases. Such a process, in which communication is based on the Fick law, was studied by Bobrowski (Ann. Henri Poincaré 13(6):1501–1510, 2012) in the space of continuous functions on the graph. His results were generalized by Banasiak et al. (Semigroup Forum 93(3):427–443, 2016). We improve, in a way that cannot be obtained using a very general tool developed recently by Engel and Kramar Fijavž (Evolut. Equ. Control Theory 8(3)3:633–661, 2019), the results of J. Banasiak et al. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00371912
Volume :
101
Issue :
3
Database :
Academic Search Index
Journal :
Semigroup Forum
Publication Type :
Academic Journal
Accession number :
147315873
Full Text :
https://doi.org/10.1007/s00233-020-10135-0