Abstract
The free boundary problem is one of the important nonlinear problems in various fields of engineering, including thermal, materials, and hydraulic engineering. In this paper, modeling of the free boundary problem in oxygen diffusion problems in biological cells and the estimation problem of oxygen concentration in biological cells are considered. To date, under the assumption that the rate of oxygen absorption in cells is constant, mathematical modeling of oxygen diffusion phenomena in biological cells has been undertaken. In a real situation, however, depending on the activity of each cell, the absorption rate of oxygen changes and the change is generally random. Thus, in this paper, considering the random change of the rate of oxygen absorption, we propose a mathematical model of oxygen diffusion in biological cells. By using the proposed model, we study the method of estimation of oxygen concentration in cells in the presence of noisy observed data at the outer layer of the skin. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(7): 53–61, 2000
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