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

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 t...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2018-11, Vol.467 (2), p.1100-1128
Main Authors: Desvillettes, Laurent, Lorenzani, Silvia
Format: Article
Language:English
Subjects:
Coagulation
Fragmentation
Homogenization
Perforated domain
Smoluchowski equations
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.07.042