Abstract
This paper deals with the homogenization of a second order parabolic operator with a large nonlinear potential and periodically oscillating coefficients of both spatial and temporal variables. Under a centering condition for the nonlinear zero-order term, we obtain the effective problem and prove a convergence result. The main feature of the homogenized equation is the appearance of a non-linear convection term.
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This research was partially supported by the GNR MOMAS (Modélisation Mathématique et Simulations numériques liées aux problèmes de gestion des déchets nucléaires) (PACEN/CNRS, ANDRA, BRGM, CEA, EDF, IRSN). G. Allaire is a member of the DEFI project at INRIA Saclay Ile-de-France and is partially supported by the Chair “Mathematical modelling and numerical simulation, F-EADS - Ecole Polytechnique - INRIA”.
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Allaire, G., Piatnitski, A. Homogenization of nonlinear reaction-diffusion equation with a large reaction term. Ann. Univ. Ferrara 56, 141–161 (2010). https://doi.org/10.1007/s11565-010-0095-z
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DOI: https://doi.org/10.1007/s11565-010-0095-z