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We study the periodic homogenization of a reaction-diffusion problem withlarge nonlinear drift and Robin boundary condition posed in an unboundedperforated domain. The nonlinear problem is associated with the hydrodynamiclimit of a totally asymmetric simple exclusion process (TASEP) governing apopulation of interacting particles crossing a domain with obstacle. We areinterested in deriving rigorously the upscaled model equations and thecorresponding effective coefficients for the case when the microscopic dynamicsare linked to a particular choice of characteristic length and time scales thatlead to an exploding nonlinear drift. The main mathematical difficulty lies inproving the two-scale compactness and strong convergence results needed for thepassage to the homogenization limit. To cope with the situation, we use theconcept of two-scale compactness with drift, which is similar to the moreclassical two-scale compactness result but it is defined now in movingcoordinates. We provide as well a strong convergence result for the correctorfunction, starting this way the search for the order of the convergence rate ofthe homogenization process for our target nonlinear drift problem.

Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary data