Non-stationary model of cerebral oxygen transport with unknown sources

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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Article number910
JournalMathematics
Volume9
Issue number8
DOIs
StatePublished - 2 Apr 2021
Externally publishedYes

Keywords

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

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