On the homogenization of nonlinear convertion-diffusion equations with oscillatory initial and forcing data

We study the behavior of oscillatory solutions to convection-diffusion problems, subject to initial and forcing data with modulated multi-scale oscillations. We determine the weak W-l,OO-limit of the solutions when the small scales of the modulations tend to zero and quantify the weak convergence rate. Moreover, in case the solution operator of the equation is compact, this weak convergence is translated into a strong one. Examples include nonlinear conservation laws and equations with nonlinear degenerate diffusion.