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.

中文翻译：

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对空间平均的脑毛细血管网络中的压力分布进行建模

在对脑毛细血管网络中的压力分布进行数学建模的背景下，研究了具有未知源强度的泊松方程的边界值问题。该问题被表述为具有有限维超定性的逆问题。证明了问题的唯一可解性。提出并实现了一种数值算法。