Convection Enhanced Diffusion and Reaction

At first we study a convection-diffusion problem with so called cellular convection. In the homogenization limit we estimate the effective diffusivity. In particular for strong convection, which is a singular limit, these estimates have the correct scaling. Secondly we study the speed enhancement for travelling waves of reaction-diffusion-convection problems of KPP and combustion type. For shear flow convection these estimates have the correct scaling in several asymptotic regimes, i.e. strong convection, small diffusion and rapid oscillations.