# American Institute of Mathematical Sciences

February  2014, 7(1): 113-125. doi: 10.3934/dcdss.2014.7.113

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

 1 Natural and Physical Sciences, Tomakomai National College of Technology, 443, Nishikioka, Tomakomai-shi, Hokkaido, 059-1275, Japan

Received  February 2012 Revised  October 2012 Published  July 2013

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.
Citation: Kota Kumazaki. A mathematical model of carbon dioxide transport in concrete carbonation process. Discrete & Continuous Dynamical Systems - S, 2014, 7 (1) : 113-125. doi: 10.3934/dcdss.2014.7.113
##### References:
 [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.  Google Scholar [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.  Google Scholar [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). Google Scholar [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.  Google Scholar [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.  Google Scholar [6] K. Maekawa, R. Chaube and T. Kishi, "Modeling of Concrete Carbonation," Taylor and Francis, 1999. Google Scholar [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.  Google Scholar [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.  Google Scholar

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##### References:
 [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.  Google Scholar [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.  Google Scholar [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). Google Scholar [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.  Google Scholar [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.  Google Scholar [6] K. Maekawa, R. Chaube and T. Kishi, "Modeling of Concrete Carbonation," Taylor and Francis, 1999. Google Scholar [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.  Google Scholar [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.  Google Scholar
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