Homogenization of nonlinear reaction-diffusion equation with a large reaction term

Grégoire Allaire; Andrey Piatnitski

doi:10.1007/s11565-010-0095-z

Homogenization of nonlinear reaction-diffusion equation with a large reaction term

Grégoire Allaire
, Andrey Piatnitski

University of Tromsø - The Arctic University of Norway
P.N. Lebedev Physical Institute of the Russian Academy of Sciences

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

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.

Original language	English
Pages (from-to)	141-161
Number of pages	21
Journal	Annali dell'Universita di Ferrara
Volume	56
Issue number	1
DOIs	https://doi.org/10.1007/s11565-010-0095-z
Publication status	Published - 12 Feb 2010

Keywords

Homogenization
Nonlinear potential
Reaction-diffusion

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10.1007/s11565-010-0095-z

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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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N2 - 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.

AB - 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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KW - Nonlinear potential

KW - Reaction-diffusion

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Homogenization of nonlinear reaction-diffusion equation with a large reaction term

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Keywords

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