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Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources

Author

Listed:
  • Andrey Kovtanyuk

    (Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany
    Klinikum Rechts der Isar, Technische Universität München, Ismaningerstr. 22, 81675 München, Germany
    Far Eastern Federal University, Sukhanova st. 8, 690950 Vladivostok, Russia)

  • Alexander Chebotarev

    (Far Eastern Federal University, Sukhanova st. 8, 690950 Vladivostok, Russia
    Institute for Applied Mathematics FEB RAS, Radio st. 7, 690041 Vladivostok, Russia)

  • Varvara Turova

    (Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany
    Klinikum Rechts der Isar, Technische Universität München, Ismaningerstr. 22, 81675 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)

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.

Suggested Citation

  • Andrey Kovtanyuk & Alexander Chebotarev & Varvara Turova & Irina Sidorenko & Renée Lampe, 2021. "Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources," Mathematics, MDPI, vol. 9(8), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:910-:d:539561
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    References listed on IDEAS

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    1. Kovtanyuk, Andrey & Chebotarev, Alexander & Turova, Varvara & Sidorenko, Irina & Lampe, Renée, 2021. "An inverse problem for equations of cerebral oxygen transport," Applied Mathematics and Computation, Elsevier, vol. 402(C).
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