A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the root t-law of propagation

作者：Aiki Toyohiko^*; Muntean Adrian

来源：Interfaces and Free Boundaries, 2013, 15(2): 167-180.

DOI：10.4171/IFB/299

• Large-time behavior
• free-boundary problem
• concrete carbonation
• integral estimates

We study a one-dimensional free-boundary problem describing the penetration of carbonation fronts (free reaction-triggered interfaces) in concrete. Using suitable integral estimates for the free boundary and involved concentrations, we reach a twofold aim: %26lt;br%26gt;(1) We fill a fundamental gap by justifying rigorously the experimentally guessed root t asymptotic behavior. Previously we obtained the upper bound s(t) %26lt;= C%26apos;root t for some constant C%26apos;; now we show the optimality of the rate by proving the right nontrivial lower estimate, i.e., there exists C %26apos;%26apos; %26gt; 0 such that s(t) %26gt;= C %26apos;%26apos; root t. %26lt;br%26gt;(2) We obtain weak solutions to the free-boundary problem for the case when the measure of the initial domain vanishes. In this way, we allow for the nucleation of the moving carbonation front - a scenario that until now was open from the mathematical analysis point of view.

• 出版日期2013