A one dimensional free boundary problem for adsorption phenomena

  • 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.

    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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  • 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.


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    [8] T. Aiki, Y. Murase, N. Sato and K. Shirawaka, A mathematical model for a hysteresis appearing in adsorption phenomena, Sūrikaisekikenkyūsho Kōkyūroku, 1856 (2013), 1-12.
    [9] A. Fasano and M. Primicerio, Free boundary problems for nonlinear parabolic equations with nonlinear free boundary conditions, J. Math. Anal. Appl., 72 (1979), 247-273. doi: 10.1016/0022-247X(79)90287-7
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  • This article has been cited by:

    1. Toyohiko Aiki, Yusuke Murase, On a large time behavior of a solution to a one-dimensional free boundary problem for adsorption phenomena, 2017, 445, 0022247X, 837, 10.1016/j.jmaa.2016.06.008
    2. Kota Kumazaki, Toyohiko Aiki, Naoki Sato, Yusuke Murase, Multiscale model for moisture transport with adsorption phenomenon in concrete materials, 2018, 97, 0003-6811, 41, 10.1080/00036811.2017.1325473
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