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

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

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BOBROWSKI, 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. 27(4), pp. 663-706. ISSN 0218-2025. eISSN 1793-6314

@article{Bobrowski2017avera-33472, title={An averaging principle for fast diffusions in domains separated by semi-permeable membranes}, year={2017}, doi={10.1142/S0218202517500130}, 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} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/33472"> <dc:contributor>Bobrowski, Adam</dc:contributor> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-05-15T13:09:57Z</dc:date> <dc:creator>Bobrowski, Adam</dc:creator> <dc:creator>Kazmierczak, Bogdan</dc:creator> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-05-15T13:09:57Z</dcterms:available> <dcterms:title>An averaging principle for fast diffusions in domains separated by semi-permeable membranes</dcterms:title> <dc:contributor>Kunze, Markus</dc:contributor> <dc:contributor>Kazmierczak, Bogdan</dc:contributor> <dcterms:issued>2017</dcterms:issued> <dc:creator>Kunze, Markus</dc:creator> <dc:language>eng</dc:language> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/33472"/> <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> </rdf:Description> </rdf:RDF>

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