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

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.

Keywords:

• corrector estimates
• periodic unfolding
• homogenization
• sulphate corrosion of concrete
• reaction–diffusion systems

AMS Subject Classifications::

• 35B27
• 47Q10
• 74Q15
• 35K57
• 35K60