# American Institute of Mathematical Sciences

doi: 10.3934/mcrf.2021016

## Modeling the pressure distribution in a spatially averaged cerebral capillary network

 1 Technische Universität München, 81675 Munich, Germany 2 Far Eastern Federal University, 690950 Vladivostok, Russia 3 Institute for Applied Mathematics, FEB RAS, 690041 Vladivostok, Russia

* Corresponding author: Andrey Kovtanyuk

Received  March 2019 Revised  March 2020 Published  March 2021

Fund Project: The work was supported by the Klaus Tschira Foundation, Buhl-Strohmaier Foundation, and Würth Foundation

A boundary value problem for the Poisson's equation with unknown intensities of sources is studied in context of mathematical modeling the pressure distribution in cerebral capillary networks. The problem is formulated as an inverse problem with finite-dimensional overdetermination. The unique solvability of the problem is proven. A numerical algorithm is proposed and implemented.

Citation: Andrey Kovtanyuk, Alexander Chebotarev, Nikolai Botkin, Varvara Turova, Irina Sidorenko, Renée Lampe. Modeling the pressure distribution in a spatially averaged cerebral capillary network. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2021016
##### References:

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##### References:
Stencil corresponding to the cubic topology
The pressure distribution
The absolute velocity distribution
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