| Abstract: |
| We consider the initial-boundary value problems for nonlinear parabolic equations describing moisture transport in a porous material occupying a one-dimensional interval. This study is strongly motivated by Fukui, Iba, Hokoi, and Ogura`s article, in which, they only reported validation of the model by comparing experimental and numerical results. Therefore, we aim to analyze this model, mathematically. We note that their system consists of two equations corresponding to conservation law for air and liquid in the region, and one equation is type of elliptic-parabolic. As a first step in this research, we simplify the model such that the mass distribution in air is given. The unknown function of our model indicates the chemical potential of water. Also, we approximate the elliptic-parabolic equation. The purpose of this talk is to establish existence and uniqueness of solutions to the approximate problem by applying the evolution equation theory and the standard fixed-point argument. This is a joint work with Toyohiko AIKI (Japan Women`s University) and EBARA Corporation, Japan. |
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