Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry's law and time-dependent Dirichlet data

TL;DR

This paper analyzes the long-term behavior of reaction fronts in concrete, extending previous models to include nonlinear Henry's law effects and time-dependent boundary conditions, providing a more comprehensive understanding of carbonation processes.

Contribution

It offers a rigorous mathematical justification for the t behavior of reaction depths considering nonlinearities and dynamic boundary data.

Findings

Reaction penetration depth follows t asymptotics.

Nonlinear Henry's law effects are incorporated into the model.

Time-dependent Dirichlet data influence the reaction front evolution.

Abstract

We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the $\sqrt{t}$-behavior of reaction penetration depths by including non-linear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data.