Homogenization results for a coupled system of reaction–diffusion equations. (November 2019)

• Record Type: Journal Article
• Authors: Cardone, G.; Perugia, C.; Timofte, C.
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 236
• Page End: 264
• Publication Date: 2019-11
• Subjects: 35B27 -- 35K57 -- 35Q92; Homogenization -- Nonlinear flux conditions -- Reaction–diffusion equations; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.06.004
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction–diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying several metabolic processes taking place in living cells, in which biochemical species can diffuse in the cytosol and react both in the cytosol and also on the organellar membranes. The coupling of the concentrations of the biochemical species is realized via various properly scaled nonlinear reaction terms. These nonlinearities, which model, at the microscopic scale, various volume or surface reaction processes, give rise in the macroscopic model to different effects, such as the appearance of additional source or sink terms or of a non-standard diffusion matrix.