The paper addresses the mathematical study of a nonstationary continuum model describing oxygen propagation in cerebral substance. The model allows to estimate the rate of oxygen saturation and stabilization of oxygen concentration in relatively large parts of cerebral tissue. A theoretical and numerical analysis of the model is performed. The unique solvability of the underlying initial-boundary value problem for a system of coupled nonlinear parabolic equations is proved. In the numerical experiment, the tissue oxygen saturation after hypoxia is analyzed for the case when a sufficient amount of oxygen begins to flow into the capillary network. A fast stabilization of the tissue oxygen concentration is demonstrated. The reliability of the results of the numerical simulation is discussed.

中文翻译：

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脑组织中氧气运输的非平稳模型。

本文介绍了描述大脑物质中氧传播的非平稳连续模型的数学研究。该模型可以估计大脑组织中相对较大部分的氧饱和度和氧浓度的稳定度。对模型进行了理论和数值分析。证明了耦合的非线性抛物方程组的初始初值问题的唯一可解性。在数值实验中，针对缺氧后组织氧饱和度进行了分析，以了解是否有足够的氧气开始流入毛细血管网络。证明了组织氧浓度的快速稳定。讨论了数值模拟结果的可靠性。