Homogenization of the discrete diffusive coagulation-fragmentation equations in perforated domains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:467

Article

Desvillettes, Laurent¹  Lorenzani, Silvia² 

[1] UPMC Univ Paris 06, Sorbonne Univ, Univ Paris Diderot,CNRS,UMR 7586, Sorbonne Paris Cite,Inst Math Jussieu Paris Rive, F-75013 Paris, France

[2] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy

关键词: Coagulation;    Fragmentation;    Smoluchowski equations;    Homogenization;    Perforated domain;   

DOI  :  10.1016/j.jmaa.2018.07.042

来源: Elsevier

【 摘 要 】

The asymptotic behavior of the solution of an infinite set of Smoluchowski's discrete coagulation-fragmentation-diffusion equations with non-homogeneous Neumann boundary conditions, defined in a periodically perforated domain, is analyzed. Our homogenization result, based on Nguetseng-Allaire two-scale convergence, is meant to pass from a microscopic model (where the physical processes are properly described) to a macroscopic one (which takes into account only the effective or averaged properties of the system). When the characteristic size of the perforations vanishes, the information given on the microscale by the non-homogeneous Neumann boundary condition is transferred into a global source term appearing in the limiting (homogenized) equations. Furthermore, on the macroscale, the geometric structure of the perforated domain induces a correction in the diffusion coefficients. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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