Asymptotic profiles for convection-diffusion equations with variable diffusion

We investigate the large time behavior of solutions of the convection-diffu sion equation u(t) - div(a(x)delu) = d . del (\u\(q-1)u) d epsilon R-N, in (0, infinity) x R-N with integrable initial data u(0)(x). We take a(x) = 1 + b(x) > 0 with b sm ooth and decaying to zero fast enough as x --> infinity. When q > 1 + 1/N, it is known that the solutions behave, in a first approximation, like the s olutions of the head equation taking the same initial data as t --> infinit y. We show here the influence of the nonlinear term and the variable diffus ion in the large time behavior by obtaining the second term in the asymptot ic development of solutions as t --> infinity. (C) 2001 Elsevier Science Lt d. All rights reserved.