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Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion

Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion

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Original languageEnglish
Pages1129-1154
Number of pages26
JournalApplicable Analysis
Journal publication date2012
Volume91
Issue6
Early online date14/10/11
DOIs
StatePublished

Abstract

We use the periodic unfolding technique to derive corrector estimates for a reaction-diffusion system describing concrete corrosion penetration in the sewer pipes. The system, defined in a periodically perforated domain, is semi-linear, partially dissipative and coupled to a nonlinear ordinary differential equation posed on the solid-water interface at the pore level. After discussing the solvability of the pore scale model, we apply the periodic unfolding techniques (adapted to treat the presence of perforations) not only to derive macroscopic (upscaled) model equations, but also to prepare a proper framework for obtaining a convergence rate (corrector estimates) of the averaging procedure.

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