Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources

Andrey Kovtanyuk, Alexander Chebotarev, Varvara Turova, Irina Sidorenko and Renée Lampe
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Andrey Kovtanyuk: Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany
Alexander Chebotarev: Far Eastern Federal University, Sukhanova st. 8, 690950 Vladivostok, Russia
Varvara Turova: Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany
Irina Sidorenko: Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany
Renée Lampe: Klinikum Rechts der Isar, Technische Universität München, Ismaningerstr. 22, 81675 München, Germany

Mathematics, 2021, vol. 9, issue 8, 1-10

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 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.

Keywords: oxygen transport in brain; nonlinear coupled parabolic equations; unique solvability; inverse problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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