Open AccessModeling the pressure distribution in a spatially averaged cerebral capillary network
Author(s) -
Andrey E. Kovtanyuk,
A. Yu. Chebotarëv,
Nikolai D. Botkin,
Varvara Turova,
Irina Sidorenko,
Renée Lampe
Publication year - 2021
Publication title -
mathematical control and related fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.658
H-Index - 21
eISSN - 2156-8472
pISSN - 2156-8499
DOI - 10.3934/mcrf.2021016
Subject(s) - overdetermination , context (archaeology) , mathematics , poisson distribution , boundary value problem , inverse problem , inverse , capillary action , distribution (mathematics) , mathematical analysis , physics , thermodynamics , statistics , geometry , paleontology , philosophy , epistemology , biology
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.