  Averaging principle for abstract non-autonomous parabolic evolution equations
governed by time-dependent family of positive sectorial operators is proved.
Apart from linear case also a nonlinear version for continuous perturbations is
provided. These results extend Henry's averaging technique to the case where
linear part of the equation depends on time and results due to Ilyin that were
for dissipative equations.47D06, 34G05, 34G20
