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

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2017

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Kazmierczak, Bogdan

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https://doi.org/10.1142/S0218202517500130
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Mathematical Models and Methods in Applied Sciences. 2017, 27(4), pp. 663-706. ISSN 0218-2025. eISSN 1793-6314. Available under: doi: 10.1142/S0218202517500130

Zusammenfassung

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.

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Fachgebiet (DDC)
510 Mathematik

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Convergence of sectorial forms and of semigroups of operators; diffusion processes; boundary and transmission conditions; Freidlin–Wentzell averaging principle; singular perturbations; signaling pathways; kinase activity; intracellular calcium dynamics; neurotransmitters

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ISO 690BOBROWSKI, Adam, Bogdan KAZMIERCZAK, Markus KUNZE, 2017. An averaging principle for fast diffusions in domains separated by semi-permeable membranes. In: Mathematical Models and Methods in Applied Sciences. 2017, 27(4), pp. 663-706. ISSN 0218-2025. eISSN 1793-6314. Available under: doi: 10.1142/S0218202517500130
BibTex
@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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