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| We consider a drying and wetting process in a porous media. In this talk we focus one hole of the media and regard the hole as a one-dimensional interval $[0,L]$. Here, at $x=0$ the wall exists and $x =L$ the air comes from outside. Also, the intervals $[0,s(t)]$ and $[s(t),L]$ indicate the water-drop region and the air region in the hole, respectively, and $u$ is the humidity in the pore. Then $u$ satisfies a diffusion equation in the non-cylindrical domain given by the free boundary $s$, and $s$ satisfies the free boundary condition. This problem was proposed in order to overcome some difficulties in our study of hysteresis appearing in concrete carbonation phenomena. The aims of the present talk are to give our modeling process for the free boundary problem, and to establish the well-posedness of the problem and a large time behavior of the solution. Moreover, we show some numerical results of the problem and discuss about possibilities of this free boundary problem as a mathematical description for hysteresis. |
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