Large‐time behavior of a two‐scale semilinear reaction–diffusion system for concrete sulfatation |
| |
Authors: | Toyohiko Aiki Adrian Muntean |
| |
Affiliation: | 1. Department of Mathematical and Physical Sciences, Faculty of Science, Japan Women's University, Tokyo 112‐8681, Japan;2. Centre for Analysis, Scientific computing and Applications (CASA), Institute for Complex Molecular Systems (ICMS), Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands |
| |
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 (or cement)‐based materials with sulfates. We prove that as t → ∞ , 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. Copyright © 2014 John Wiley & Sons, Ltd. |
| |
Keywords: | large‐time asymptotics two‐scale system reaction– diffusion system concrete corrosion homogenization |
|
|