Homogenization of a nonlinear convectiondiffusion equation with rapidly oscillating coefficients and strong convection

A Cauchy problem for a nonlinear convection-diffusion equation with periodic rapidly oscillating coefficients is studied. Under the assumption that the convection term is large, it is proved that the limit (homogenized) equation is a nonlinear diffusion equation which shows dispersion effects. The convergence of the homogenization procedure is justified by using a new version of a two-scale convergence technique adapted to rapidly moving coordinates. 1