Large time behavior for convection-diffusion equations in R-N with periodic coefficients

Ws describe the large time behavior of solutions of the convection-diffusio n equation u(t) - div(u(N) delu) = d . del(\u\(q-1) u) in (0, infinity) x R-N where d is an element of R-N and a = a(x) is a symmetric periodic matrix sa tisfying suitable ellipticity assumptions. We also assume that a is an elem ent of W-1,W- chi(R-N). First, we consider the linear problem (d = 0) and p rove that the large time behavior of solutions is given by the fundamental solution of the diffusion equation with a equivalent to a(h) where a(h) is the homogenized matrix. In the nonlinear case, when q = 1 + 1/N, we prove t hat the large time behavior of solutions with initial data in L-1(R-N) is g iven by a uniparametric family of semi-similar solutions of the convection- diffusion equation with constant homogenized diffusion a equivalent to a(h) . When q > 1 + 1/N, we prove that the large time behavior of solutions is g iven by the fundamental solution of the linear-diffusion equation with a eq uivalent to a(h). (C) 2000 Academic Press.