In:
Mathematical Models and Methods in Applied Sciences, World Scientific Pub Co Pte Ltd, Vol. 27, No. 04 ( 2017-04), p. 663-706
Abstract:
We prove an averaging principle which asserts convergence of diffusion processes on domains separated by semi-permeable membranes, when diffusion coefficients tend to infinity while the flux through the membranes remains constant. In the limit, points in each domain are lumped into a single state of a limit Markov chain. The limit chain’s intensities are proportional to the membranes’ permeability and inversely proportional to the domains’ sizes. Analytically, the limit is an example of a singular perturbation in which boundary and transmission conditions play a crucial role. This averaging principle is strongly motivated by recent signaling pathways models of mathematical biology, which are discussed toward the end of the paper.
Type of Medium:
Online Resource
ISSN:
0218-2025
,
1793-6314
DOI:
10.1142/S0218202517500130
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2017
SSG:
11
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