Pressure spatial decomposition @model

Reverse the problem to spatial superposition where pressure response  $//<![CDATA[ \begin{array}{l}p_m(t)\end{array} //]]>$ in  $//<![CDATA[ \begin{array}{l}m\end{array} //]]>$-well is decomposed into a sum of individual pressure responses from :

where  $//<![CDATA[ \begin{array}{l}\delta p_{mk}(t)\end{array} //]]>$ is a specific component of  $//<![CDATA[ \begin{array}{l}m\end{array} //]]>$-well pressure variation caused by  $//<![CDATA[ \begin{array}{l}k\end{array} //]]>$-well flowrate history  $//<![CDATA[ \begin{array}{l}q_k(t)\end{array} //]]>$,

and  $//<![CDATA[ \begin{array}{l}p_{ukm}(\tau)\end{array} //]]>$ is a pressure response in $//<![CDATA[ \begin{array}{l}m\end{array} //]]>$-well to unit-rate drawdown in $//<![CDATA[ \begin{array}{l}k\end{array} //]]>$-well 

The ultimate problem is to find transient responses  $//<![CDATA[ \begin{array}{l}p_{ukm}(\tau)\end{array} //]]>$ for cross-well intervals.