混凝土腐蚀预测的反应扩散系统的基于展开的校正估计
Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion
摘要：
我们使用的周期性展开技术来获得校正估计的反应扩散系统描述混凝土腐蚀渗透在下水道管道。该系统，定义在一个多孔的域，是半线性的，部分耗散的，并通过一个非线性常微分方程耦合的固体-水界面上的孔隙水平。在讨论了孔隙尺度模型的可解性之后，我们应用周期性展开技术（适于处理穿孔的存在）不仅得到放大的模型方程，而且还准备了一个适当的框架，用于获得平均过程的收敛速度（校正估计）。
英文摘要：
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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