Abstract
AbstractWe study a diffusion process on a finite graph with semipermeable membranes on vertices. We prove, in $$L^1$$
L
1
and $$L^2$$
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.
Funder
Lublin University of Technology
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Concatenation of Nonhonest Feller Processes, Exit Laws, and Limit Theorems on Graphs;SIAM Journal on Mathematical Analysis;2023-08-14
2. Nonsmooth Optimization for Synaptic Depression Dynamics;2022 8th International Conference on Optimization and Applications (ICOA);2022-10-06
3. Hemivariational inequalities on graphs;Computational and Applied Mathematics;2022-05-13