  Controlling the spin dynamics and spin lifetimes is one of the main
challenges in spintronics. To this end, the study of the spin diffusion in
two-dimensional electron gases (2DEGs) shows that when the Rashba and
Dresselhaus spin-orbit couplings (SOC) are balanced, a persistent spin helix
regime arises. There, a striped spin pattern shows a long lifetime, limited
only by the cubic Dresselhaus SOC, and its dynamics can be controlled by
in-plane drift fields. Here, we derive a spin diffusion equation for
non-degenerate two-subbands 2DEGs. We show that the intersubband scattering
rate, which is defined by the overlap of the subband densities, enters as a new
nob to control the spin dynamics, and can be controlled by electric fields,
being maximum for symmetric quantum wells. We find that for large intersubband
couplings the dynamics follow an effective diffusion matrix given by
approximately half of the subband-averaged matrices. This extra 1/2 factor
arises from Matthiessen's rule summing over the intra- and intersubband
scattering rates, and leads to a reduced diffusion constant and larger spin
lifetimes. We illustrate our findings with numerical solutions of the diffusion
equation with parameters extracted from realistic Schr\"odinger-Poisson
calculations.
