For the pressure diffusion with constant diffusion coefficients and homogeneous boundary conditions the pressure response in one well to a complex flowrate history in the same well honours the convolution equation:
p(t) = p_0 + \int_0^t p_u(t-\tau) \, dq(\tau) |
In case a well is interferring with the offset wells the pressure in a given well may respond to the offset wells and the multi-well form of convolutions is going to be:
p_n(t) = p_{n, 0} + \sum_{m=1}^N \int_0^t p_{u,nm}(t-\tau) \, dq_m(\tau) |