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

Tasnim Fatima, Adrian Muntean, Mariya Ptashnyk

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    24 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)1129-1154
    Number of pages26
    JournalApplicable Analysis
    Volume91
    Issue number6
    Early online date14 Oct 2011
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Corrector estimates
    • Periodic unfolding
    • Homogenization
    • Sulphate corrosion of concrete
    • Reaction-diffusion systems

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