On development of analytical method for mathematical models including hysteresis and study of the suitability of the models
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
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
|
Keywords | 自由境界問題 / ヒステリシス / コンクリート中性化 / 解の漸近収束 / 準線形放物型方程式 / 無限大での解の挙動 / コンクリートの中性化 / コンクリートの腐食 / two-scale problem |
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.
|
Report
(4 results)
Research Products
(40 results)