On development of analytical method for mathematical models including hysteresis and study of the suitability of the models

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540209
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global 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): MURASE Yusuke 名城大学, 理工学部, 助教 (80546771)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 自由境界問題 / ヒステリシス / コンクリート中性化

Outline of Final Research Achievements

In a study for the system of nonlinear partial differential equations describing concrete carbonation process and dynamics of shape memory alloy material it was not easy to obtain the well posedness of the system because of the difficulty of mathematical treatment for hysteresis. In this research project by applying the classical theory for nonlinear partial differential equations we can show the uniqueness of a solution to the initial boundary value problem for the system. Also, we obtain the well posedness and a result on large time behavior of a solution to a mathematical multi-scale model describing a concrete corrosion process. We have an idea to deal with hysteresis by using multi-scale modeling motivated by the study for concrete corrosion problem so that we have proposed a free boundary problem as a mathematical model for adsorption phenomenon, and proved the global existence in time and the uniqueness of a solution to the problem.

Free Research Field

非線形偏微分方程式