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) = p_0 + \int_0^t p_u(t-\tau) \, \dot q(\tau) \, d\tau 

where

	initial formation pressure at zero time
	Drawdown Transient Response
	a pace of sandface flow rate variation per unit time

In case a well is interfering with the offset wells the pressure in a given well   may respond to the offset wells  and the multi-well form of convolution 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) = p_{n, 0} + \sum_{m=1}^N \int_0^t p_{u,nm}(t-\tau) \, \dot q_m(\tau) \, d\tau

where

	initial formation pressure at zero time for the -th well
	Cross-well Transient Response in the -th well to the flow variation in -th well
	a pace of sandface flow rate variation of the -th well per unit time