Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation

TL;DR

This paper investigates the long-term behavior of a two-scale reaction-diffusion system modeling concrete sulfate corrosion, proving convergence to a stationary state using advanced evolution equation theory and energy estimates.

Contribution

It introduces a novel analysis of the large-time dynamics of a coupled two-scale system with nonlinear ODEs, establishing convergence to equilibrium.

Findings

Solutions converge to stationary states as time approaches infinity

The analysis employs subdifferential operator theory and energy estimates

Provides a rigorous mathematical framework for concrete sulfate corrosion modeling

Abstract

We study the large-time behavior of (weak) solutions to a two-scale reaction-diffusion system coupled with a nonlinear ordinary differential equations modeling the partly dissipative corrosion of concrete (/cement)-based materials with sulfates. We prove that as $t\to\infty$ the solution to the original two-scale system converges to the corresponding two-scale stationary system. To obtain the main result we make use essentially of the theory of evolution equations governed by subdifferential operators of time-dependent convex functions developed combined with a series of two-scale energy-like time-independent estimates.