Asymptotic profiles for convection–diffusion equations with variable diffusion Original Research Article

We investigate the large time behavior of solutions of the convection-diffusion equation View the MathML source with integrable initial data u0(x). We take a(x)=1+b(x)>0 with b smooth and decaying to zero fast enough as x→∞. When View the MathML source, it is known that the solutions behave, in a first approximation, like the solutions of the head equation taking the same initial data as t→∞. We show here the influence of the nonlinear term and the variable diffusion in the large time behavior by obtaining the second term in the asymptotic development of solutions as t→∞.