Uniqueness of solutions to a mathematical model describing moisture transport in
concrete materials
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1.
Department of Mathematical and Physical Sciences, Faculty of Science, Japan Women's University, 2-8-1 Mejirodai, Bunkyo-ku, Tokyo 112-8681
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2.
Natural and Physical Sciences, Tomakomai National College of Technology, 443, Nishikioka, Tomakomai-shi, Hokkaido, 059-1275
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Received:
01 June 2014
Revised:
01 August 2014
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Primary: 74H25, 35K55; Secondary: 47J40.
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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.
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.
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