A one dimensional free boundary problem for adsorption phenomena

Naoki Sato; Toyohiko Aiki; Yusuke Murase; Ken Shirakawa; Naoki Sato; Toyohiko Aiki; Yusuke Murase; Ken Shirakawa

doi:10.3934/nhm.2014.9.655

Networks and Heterogeneous Media

2014, Volume 9, Issue 4: 655-668. doi: 10.3934/nhm.2014.9.655

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A one dimensional free boundary problem for adsorption phenomena

1.
Division of General Education, Nagaoka National College of Technology, 888, Nishikatakai, Nagaoka, Niigata, 940-8532
2.
Japan Woman's University, Department of Mathematics and Physical Sciences, Faculty of Science, 2-8-1 Mejirodai, Bunkyo-ku, Tokyo 112-8681
3.
Department of Mathematics, Faculty of Science and Technology, Meijo University, 1-501 Shiogamaguchi, Tenpaku-ku, Nagoya, 468-8502
4.
Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522

Received: 01 February 2014 Revised: 01 September 2014
Primary: 35R35; Secondary: 35K61, 74F25.

In this paper we deal with a one-dimensional free boundary problem, which is a mathematical model for an adsorption phenomena appearing in concrete carbonation process. This model was proposed in line of previous studies of three dimensional concrete carbonation process. The main result in this paper is concerned with the existence and uniqueness of a time-local solution to the free boundary problem. This result will be obtained by means of the abstract theory of nonlinear evolution equations and Banach's fixed point theorem, and especially, the maximum principle applied to our problem will play a very important role to obtain the uniform estimate to approximate solutions.
- Free boundary problem,
- drying and wetting process
Citation: Naoki Sato, Toyohiko Aiki, Yusuke Murase, Ken Shirakawa. A one dimensional free boundary problem for adsorption phenomena[J]. Networks and Heterogeneous Media, 2014, 9(4): 655-668. doi: 10.3934/nhm.2014.9.655

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Abstract

In this paper we deal with a one-dimensional free boundary problem, which is a mathematical model for an adsorption phenomena appearing in concrete carbonation process. This model was proposed in line of previous studies of three dimensional concrete carbonation process. The main result in this paper is concerned with the existence and uniqueness of a time-local solution to the free boundary problem. This result will be obtained by means of the abstract theory of nonlinear evolution equations and Banach's fixed point theorem, and especially, the maximum principle applied to our problem will play a very important role to obtain the uniform estimate to approximate solutions.

References

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