This image shows a minimal example of a system of equations that allows us to demonstrate the essence of several questions. 
These equations are taken from the article.
Main questions:
- When the authors find the partial derivative $\bar{p}_{Df}$ with respect to the $x_D$ coordinate at point $x_D = 1$ (B-16 formula), they do not indicate that the function $\bar{p}_{D1s}$ must also be calculated at this point. I believe this is incorrect.
- $\bar{p}_{D1s}(x_D, s)$ depends on $\bar{p}_{Df}(x_D, s)$. To find the value of the function $\bar{p}_{D1s}$ in formula (B-18), the authors use averaging $\bar{p}_{Df}$ (D-11) over the domain of definition of the function, while in my opinion the function $\bar{p}_{D1s}$ should have been calculated at the $x_D = 1$, which corresponds to the $x_D$ point in the region ''f'' . Is the approach of the authors correct?
- When the authors carry out the integration of a $\bar{p}_{Df}$ (D-10, D-11) over a given area $x_D \subset [0,1]$, they seem to assume that the $\bar{p}_{D1s}(x_D, s)$ is a constant value (this can be seen from the results of the formula D-11), which, in my opinion, is not correct. Tell me, is this a mistake, or is it somehow possible to prove?