Open AccessScaling effects on the periodic homogenization of a reaction-diffusion-convection problem posed in homogeneous domains connected by a thin composite layer
Author(s) -
Vishnu Raveendran,
Emilio N. M. Cirillo,
Ida de Bonis,
Adrian Muntean
Publication year - 2021
Publication title -
quarterly of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.603
H-Index - 41
eISSN - 1552-4485
pISSN - 0033-569X
DOI - 10.1090/qam/1607
Subject(s) - homogenization (climate) , scaling , mathematics , scaling limit , mathematical analysis , thin layer , homogeneous , limit (mathematics) , composite number , statistical physics , layer (electronics) , materials science , physics , geometry , algorithm , nanotechnology , biodiversity , ecology , biology
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.