\frac{\partial p}{\partial t} = \chi \, \left[  \frac{\partial^2 p}{\partial t^2} + \frac{1}{r} \frac{\partial p}{\partial r} \right]

p(t=0,r) = p_i

p(t, r=\infty) = p_i

\left[ r \frac{\partial p}{\partial r} \right]_{r=0} = - \frac{q_t}{2 \pi \sigma}