  We follow-up on our works devoted to homogenization theory for linear
second-order elliptic equations with coefficients that are perturbations of
periodic coefficients. We have first considered equations in divergence form in
[6, 7, 8]. We have next shown, in our recent work [9], using a slightly
different strategy of proof than in our earlier works, that we may also address
the equation --aij$\partial$iju = f. The present work is devoted to
advection-diffusion equations: --aij$\partial$iju + bj$\partial$ju = f. We
prove, under suitable assumptions on the coefficients aij, bj, 1 $\le$ i, j
$\le$ d (typically that they are the sum of a periodic function and some
perturbation in L p , for suitable p < +$\infty$), that the equation admits a
(unique) invariant measure and that this measure may be used to transform the
problem into a problem in divergence form, amenable to the techniques we have
previously developed for the latter case.
