Upscaling of a parabolic system with a large nonlinear surface reaction term |
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Authors: | Renata Bunoiu Claudia Timofte |
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Institution: | 1. University of Lorraine, CNRS, IECL, F-57000, Metz, France;2. University of Bucharest, Faculty of Physics, Bucharest-Magurele, P.O. Box MG-11, Romania |
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Abstract: | Motivated by the study of the dynamics of calcium ions in biological cells, the authors derived in 33], via periodic homogenization, a macroscopic bidomain model, by considering in the corresponding microscopic two-component problem a properly scaled nonlinear exchange term. We study here, at the microscopic scale, a similar parabolic system, with a large nonlinear interfacial reaction term. At the macroscopic scale, the nonlinear effect of this reaction term is recovered in the homogenized diffusion matrix, which is not anymore constant. This nonstandard phenomenon shows the fine interplay between reaction and diffusion in such processes. |
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Keywords: | Homogenization Fast reaction Nonlinear transmission conditions |
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