@article{Bobrowski2017avera-33472,
  year={2017},
  doi={10.1142/S0218202517500130},
  title={An averaging principle for fast diffusions in domains separated by semi-permeable membranes},
  number={4},
  volume={27},
  issn={0218-2025},
  journal={Mathematical Models and Methods in Applied Sciences},
  pages={663--706},
  author={Bobrowski, Adam and Kazmierczak, Bogdan and Kunze, Markus}
}

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    <dc:contributor>Kazmierczak, Bogdan</dc:contributor>
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    <dcterms:abstract xml:lang="eng">We prove an averaging principle which asserts convergence of diffusions on domains separated by semi-permeable membranes, when the speed of diffusion tends 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 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 in the final section of the paper.</dcterms:abstract>
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