Leonid Koralov (Maryland)

Transition from homogenization to averaging in cellular flows

Abstract: We consider an elliptic problem that involves two parameters (the size of the domain, which may be
large, and the magnitude of the diffusion coefficient, which may be small). Depending on the relation between the
parameters, the asymptotics of the solution is given either by homogenization theory or by averaging.
Using probabilistic techniques, we give a precise description of the transition regime, where a more intricate
behavior is observed.