Mathematical Model

(1)	$\begin{array}{l}\displaystyle \frac{\partial p}{\partial t} = \chi \, \left[ \frac{\partial^2 p}{\partial t^2} + \frac{1}{r} \frac{\partial p}{\partial r} \right]\end{array}$

(2)	$\begin{array}{l}\displaystyle p(t=0,r) = p_i\end{array}$

(3)	$\begin{array}{l}\displaystyle p(t, r=\infty) = p_i\end{array}$

(4)	$\begin{array}{l}\displaystyle \left[ r \frac{\partial p}{\partial r} \right]_{r=0} = - \frac{q_t}{2 \pi \sigma}\end{array}$

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See also