Non-stationary model of cerebral oxygen transport with unknown sources

Andrey Kovtanyuk; Alexander Chebotarev; Varvara Turova; Irina Sidorenko; Renée Lampe

doi:10.3390/math9080910

Non-stationary model of cerebral oxygen transport with unknown sources

Andrey Kovtanyuk, Alexander Chebotarev, Varvara Turova, Irina Sidorenko, Renée Lampe

Associate Professorship of Paediatric Neuroorthopaedics, Main Research: Cerebral Palsy

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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 concen-tration 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.

Original language	English
Article number	910
Journal	Mathematics
Volume	9
Issue number	8
DOIs	https://doi.org/10.3390/math9080910
State	Published - 2 Apr 2021

Keywords

Inverse problem
Nonlinear coupled parabolic equations
Oxygen transport in brain
Unique solvability

Access to Document

10.3390/math9080910

Cite this

@article{8e5153dd6a5b43d88fa60d54ec3eb5bf,

title = "Non-stationary model of cerebral oxygen transport with unknown sources",

abstract = "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 concen-tration 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.",

keywords = "Inverse problem, Nonlinear coupled parabolic equations, Oxygen transport in brain, Unique solvability",

author = "Andrey Kovtanyuk and Alexander Chebotarev and Varvara Turova and Irina Sidorenko and Ren{\'e}e Lampe",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors, Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = apr,

day = "2",

doi = "10.3390/math9080910",

language = "English",

volume = "9",

journal = "Mathematics",

issn = "2227-7390",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "8",

}

TY - JOUR

T1 - Non-stationary model of cerebral oxygen transport with unknown sources

AU - Kovtanyuk, Andrey

AU - Chebotarev, Alexander

AU - Turova, Varvara

AU - Sidorenko, Irina

AU - Lampe, Renée

PY - 2021/4/2

Y1 - 2021/4/2

N2 - 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 concen-tration 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.

AB - 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 concen-tration 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.

KW - Inverse problem

KW - Nonlinear coupled parabolic equations

KW - Oxygen transport in brain

KW - Unique solvability

UR - http://www.scopus.com/inward/record.url?scp=85105204814&partnerID=8YFLogxK

U2 - 10.3390/math9080910

DO - 10.3390/math9080910

M3 - Article

AN - SCOPUS:85105204814

SN - 2227-7390

VL - 9

JO - Mathematics

JF - Mathematics

IS - 8

M1 - 910

ER -

Non-stationary model of cerebral oxygen transport with unknown sources

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this