Upscaling of a parabolic system with a large nonlinear surface reaction term

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:469

Article

Bunoiu, Renata¹  Timofte, Claudia² 

[1] Univ Lorraine, CNRS, IECL, F-57000 Metz, France

[2] Univ Bucharest, Fac Phys, POB MG-11, Bucharest, Romania

关键词: Homogenization;    Fast reaction;    Nonlinear transmission conditions;   

DOI  :  10.1016/j.jmaa.2018.09.028

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free