Uniqueness of solutions to a mathematical model describing moisture transport in
       concrete materials

Toyohiko Aiki; Kota Kumazaki; Toyohiko Aiki; Kota Kumazaki

doi:10.3934/nhm.2014.9.683

Networks and Heterogeneous Media

2014, Volume 9, Issue 4: 683-707. doi: 10.3934/nhm.2014.9.683

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Uniqueness of solutions to a mathematical model describing moisture transport in concrete materials

Toyohiko Aiki ^{1
,},
Kota Kumazaki ^{2
,}

1.
Department of Mathematical and Physical Sciences, Faculty of Science, Japan Women's University, 2-8-1 Mejirodai, Bunkyo-ku, Tokyo 112-8681
2.
Natural and Physical Sciences, Tomakomai National College of Technology, 443, Nishikioka, Tomakomai-shi, Hokkaido, 059-1275

Received: 01 June 2014 Revised: 01 August 2014
Primary: 74H25, 35K55; Secondary: 47J40.

When dealing with concrete materials it is always a big issue how to deal with the moisture transport. Here, we consider a mathematical model for moisture transport, which is given as a system consisting of the diffusion equation for moisture and of the ordinary differential equation which describes a hysteresis operator. In [3] we already proved the existence of a time global solution of an initial boundary value problem of this system, however, the uniqueness is obtained only for one dimensional domains. The main purpose of this paper is to establish the uniqueness of a solution of our problem in three dimensional domains under the assumption of the smooth boundary and initial data.
- Uniqueness of solutions,
- nonlinear parabolic equations,
- equations with hysteresis operator
Citation: Toyohiko Aiki, Kota Kumazaki. Uniqueness of solutions to a mathematical model describing moisture transport in concrete materials[J]. Networks and Heterogeneous Media, 2014, 9(4): 683-707. doi: 10.3934/nhm.2014.9.683

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Abstract

When dealing with concrete materials it is always a big issue how to deal with the moisture transport. Here, we consider a mathematical model for moisture transport, which is given as a system consisting of the diffusion equation for moisture and of the ordinary differential equation which describes a hysteresis operator. In [3] we already proved the existence of a time global solution of an initial boundary value problem of this system, however, the uniqueness is obtained only for one dimensional domains. The main purpose of this paper is to establish the uniqueness of a solution of our problem in three dimensional domains under the assumption of the smooth boundary and initial data.

References

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