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

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

2011-06-16

arxiv.org/abs/1106.3233v2

Mathematics

Analysis of PDEs

23 pages, one figure

Scientific paper

10.1080/00036811.2011.625016

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 via a non-linear 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 get upscaled model equations, but also to prepare a proper framework for getting a convergence rate (corrector estimates) of the averaging procedure.

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