Scaling effects on the periodic homogenization  of a reaction-diffusion-convection problem posed in homogeneous domains connected by a thin composite layer

• We study the question of periodic homogenization of a variably scaled reaction-diffusion problem with non-linear drift posed for a domain crossed by a flat composite thin layer. The structure of the non-linearity in the drift was obtained in earlier works as hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) for a population of interacting particles crossing a domain with obstacle.Using energy-type estimates as well as concepts like thin-layer convergence and two-scale convergence, we derive the homogenized evolution equation and the corresponding effective model parameters for a regularized problem. Special attention is paid to the derivation of the effective transmission conditions across the separating limit interface in essentially two different situations: (i) finitely thin layer and (ii) infinitely thin layer.This study should be seen as a preliminary step needed for the investigation of averaging fast non-linear drifts across material interfaces—a topic with direct applications in the design of thin composite materials meant to be impenetrable to high-velocity impacts.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

non-linear drift

thin-layer convergence

periodic homogenization

reaction-diffusion problem

Matematik

Mathematics

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