Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources

Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources

An inverse problem for a system of equations modeling oxygen transport in the brain is studied. The problem consists of finding the right-hand side of the equation for the blood oxygen transport, which is a linear combination of given functionals describing the average oxygen concentration in the ne...

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Main Authors: Andrey Kovtanyuk, Alexander Chebotarev, Varvara Turova, Irina Sidorenko, Renée Lampe
Format: Article
Language:English
Published: MDPI AG 2021-04-01
Series:Mathematics
Subjects:
oxygen transport in brain
nonlinear coupled parabolic equations
unique solvability
inverse problem
Online Access:https://www.mdpi.com/2227-7390/9/8/910
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spelling doaj-24a8e84df55f4d3fbaaf93e8b4d3dfb72021-04-20T23:02:18ZengMDPI AGMathematics2227-73902021-04-01991091010.3390/math9080910Non-Stationary Model of Cerebral Oxygen Transport with Unknown SourcesAndrey Kovtanyuk0Alexander Chebotarev1Varvara Turova2Irina Sidorenko3Renée Lampe4Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, GermanyFar Eastern Federal University, Sukhanova st. 8, 690950 Vladivostok, RussiaFakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, GermanyFakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, GermanyKlinikum Rechts der Isar, Technische Universität München, Ismaningerstr. 22, 81675 München, GermanyAn inverse problem for a system of equations modeling oxygen transport in the brain is studied. The problem consists of finding the right-hand side of the equation for the blood oxygen transport, which is a linear combination of given functionals describing the average oxygen concentration in the neighborhoods of the ends of arterioles and venules. The overdetermination condition is determined by the values of these functionals evaluated on the solution. The unique solvability of the problem is proven without any smallness assumptions on the model parameters.https://www.mdpi.com/2227-7390/9/8/910oxygen transport in brainnonlinear coupled parabolic equationsunique solvabilityinverse problem
collection DOAJ
language English
format Article
sources DOAJ
author Andrey Kovtanyuk
Alexander Chebotarev
Varvara Turova
Irina Sidorenko
Renée Lampe
spellingShingle Andrey Kovtanyuk
Alexander Chebotarev
Varvara Turova
Irina Sidorenko
Renée Lampe
Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources
Mathematics
oxygen transport in brain
nonlinear coupled parabolic equations
unique solvability
inverse problem
author_facet Andrey Kovtanyuk
Alexander Chebotarev
Varvara Turova
Irina Sidorenko
Renée Lampe
author_sort Andrey Kovtanyuk
title Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources
title_short Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources
title_full Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources
title_fullStr Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources
title_full_unstemmed Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources
title_sort non-stationary model of cerebral oxygen transport with unknown sources
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-04-01
description An inverse problem for a system of equations modeling oxygen transport in the brain is studied. The problem consists of finding the right-hand side of the equation for the blood oxygen transport, which is a linear combination of given functionals describing the average oxygen concentration in the neighborhoods of the ends of arterioles and venules. The overdetermination condition is determined by the values of these functionals evaluated on the solution. The unique solvability of the problem is proven without any smallness assumptions on the model parameters.
topic oxygen transport in brain
nonlinear coupled parabolic equations
unique solvability
inverse problem
url https://www.mdpi.com/2227-7390/9/8/910
work_keys_str_mv AT andreykovtanyuk nonstationarymodelofcerebraloxygentransportwithunknownsources
AT alexanderchebotarev nonstationarymodelofcerebraloxygentransportwithunknownsources
AT varvaraturova nonstationarymodelofcerebraloxygentransportwithunknownsources
AT irinasidorenko nonstationarymodelofcerebraloxygentransportwithunknownsources
AT reneelampe nonstationarymodelofcerebraloxygentransportwithunknownsources
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