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Homogenization of a nonlinear convection-diffusion 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.

homogenization ; convection-diffusion equation ; rapidly oscillating cofficients ; two-scale convergence

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