Article Contents
Article Contents

# A mathematical model of carbon dioxide transport in concrete carbonation process

• In this paper we prove the existence of a solution for a mathematical model of carbon dioxide transport in concrete carbonation process. This model is a parabolic type equation with a nonlinear perturbation such that a coefficient of the time derivative contains a non-local term depending on the unknown function itself.
Mathematics Subject Classification: 35K55.

 Citation:

•  [1] T. Aiki and K. Kumazaki, Mathematical model for hysteresis phenomenon in moisture transport in concrete carbonation process, Phys. B, 407 (2012), 1424-1426.doi: 10.1016/j.physb.2011.10.016. [2] T. Aiki and K. Kumazaki, Well-posedness of a mathematical model for moisture transport appearing in concrete carbonation process, Adv. Math. Sci. Appl., 21 (2011), 361-381. [3] T. Aiki and A. Muntean, A free boundary problem for concrete carbonation: Rigorous justification of $\sqrtt$ -law of propagation, to appear in Interfaces and Free Boundaries, (2013). [4] T. Aiki and A. Muntean, Large time behavior of solutions to concrete carbonation problem, Commun. Pure Appl. Anal., 9 (2010), 1117-1129.doi: 10.3934/cpaa.2010.9.1117. [5] O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasi-Linear Equations of Parabolic Type," Transl. Math. Monogr., 23, Amer. Math. Soc., Providence, R. I., 1968. [6] K. Maekawa, R. Chaube and T. Kishi, "Modeling of Concrete Carbonation," Taylor and Francis, 1999. [7] K. Maekawa, T. Ishida and T. Kishi, Multi-scale modeling of concrete performance, J. Adv. Concr. Technol., 1 (2003), 91-126.doi: 10.3151/jact.1.91. [8] A. Muntean and M. Böhm, A moving boundary problem for concrete carbonation: Global existence and uniqueness of solutions, J. Math. Anal. Appl., 350 (2009), 234-251.doi: 10.1016/j.jmaa.2008.09.044.