Q^{\downarrow}_{AQ}= B \cdot \int_0^t W_{eD}(t - \tau) \dot p d\tau

q^{\downarrow}_{AQ}(t)= \frac{dQ^{\downarrow}_{AQ}}{dt}

W_{eD}(t)= \int_0^{t} \frac{\partial p_1}{\partial r_D} \bigg|_{r_D = 1} dt_D 

\frac{\partial p_1}{\partial t_D} =  \frac{\partial^2 p_1}{\partial r_D^2} + \frac{1}{r_D}\cdot \frac{\partial p_1}{\partial r_D}

p_1(t_D = 0, r_D)= 0

\frac{\partial p_1}{\partial r_D} 
\bigg|_{(t_D, r_D=r_a/r_e)} = 0