Analysis for multi-scale models describing nonlinear phenomena in porous media

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04969
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Japan Women's University
• Principal Investigator: Aiki Toyohiko 日本女子大学, 理学部, 教授 (90231745)
• Co-Investigator(Kenkyū-buntansha): 熊崎 耕太 苫小牧工業高等専門学校, 創造工学科, 准教授 (30634563) ; 村瀬 勇介 名城大学, 理工学部, 助教 (80546771)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 自由境界問題 / マルチスケールモデル

Outline of Final Research Achievements

We have established global existence of a solution to the free boundary problem describing a relationship between the degree of saturation and relative humidity in porous media. By applying this result, we have proved convergence to a steady solution, existence of a periodic solution, and a continuity of solutions of the free boundary problem with varying boundary data by some parameter. Furthermore, we can get a solution, locally in time, of a multi-scale model corresponding to mass conservation law of water in porous media.
Also, we generalized the model describing the relationship by the ordinary differential equation and proved existence of a solution to an optimal control problem. Moreover, we have proposed a new free boundary problem for swelling phenomena in porous media and obtained its local solution in time.

Free Research Field

数理モデル，非線形偏微分方程式