 «THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

## Global Existence of a Solution for a Multiscale Model Describing Moisture Transport in Concrete Materials

Author(s)
K. Kumazaki
Abstract

In the previous study  we proved the existence of a solution locally in time for a two-scale problem which is given as a mathematical model for moisture transport arising in a concrete carbonation process. The two-scale model consists of a diffusion equation of the relative humidity in a macro domain and the free boundary problems describing a wetting and drying process in infinite micro domains. In this paper, by improving the diffusion equation of the relative humidity based on the experimental result [3; 10], we construct a globally-in-time solution of the two scale model. For the global existence, we obtain uniform estimates and uniform boundedness of the solution with respect to time and use the method of extending local solutions.

Kota Kumazaki, Doctor of Philosophy (Mathematics), Associate Professor, Department of Education, Nagasaki University, 1-14, Bunkyo-cho, Nagasaki, 852-8521, Japan; e-mail: k.kumazaki@nagasaki-u.ac.jp

For citation

Kumazaki K. Global Existence of a Solution for a Multiscale Model Describing Moisture Transport in Concrete Materials. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 28, pp. 69-84. https://doi.org/10.26516/1997-7670.2019.28.69

Keywords
two-scale model, free boundary problem, quasilinear parabolic equation, moisture transport
UDC
518.517
MSC
35R35, 35K49, 76S05
DOI
https://doi.org/10.26516/1997-7670.2019.28.69
References
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