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arXiv · 1603.00494

An averaging principle for fast diffusions in domains separated by semi-permeable membranes

Adam Bobrowski·Bogdan Kazmierczak·Markus Kunze
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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 towards the end of the paper.

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Adam Bobrowski, Bogdan Kazmierczak, Markus Kunze. 2016-02-28. An averaging principle for fast diffusions in domains separated by semi-permeable membranes. https://doi.org/10.1142/s0218202517500130

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