2003 Fiscal Year Final Research Report Summary
Analysis of nonlinear phenomena describing hysteresis operators
| Project/Area Number |
14540169
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Gifu University |
|---|
Principal Investigator |
AIKI Toyohiko Gifu University, Faculty of Education, Associate Professor, 教育学部, 助教授 (90231745)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
YAMADA Masahiro Gifu University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00263666)
SATO Naoki Nagaoka College of Technology, Liberal Arts, Associate Professor, 一般教育科, 助教授 (90280370)
TAKEUCHI Shigeru Gifu University, Faculty of Education, Professor, 教育学部, 教授 (30021330)
ITO Akio Kinki University, Faculty of Engineering, Lecturer, 工学部, 講師 (30303506)
ISHIWATA Tetsuya Gifu University, Faculty of Education, Associate Professor, 教育学部, 助教授 (50334917)
|
|---|
| Project Period (FY) |
2002 – 2003
|
| Keywords | hysteresis operator / shape memory alloy / nonlinear PDE / ferromagnetic / weak solution of PDE |
|---|
| Research Abstract |
[Shape memory alloy problems] : In the dynamics of shape memory alloy materials the relationship between the strain and the stress can not be described by a usual function, and is represented by a hysteresis operator. Here, the main idea of this research project is to describe the relationship by using a general stop operator. Moreover, we consider the ordinary differential equation, which is equivalent to the generalized stop operator, and propose a system describing the dynamics of shape memory alloys. The system consists of partial differential equations and the ordinary differential equation and is studied in this project. We consider the one-dimensional problem, in which we dealt the ordinary differential equation without an approximation. In this case the regularity of a solution to the ordinary differential equation is not enough in space so that it is impossible to prove the existence of a classical solution. Then we showed the existence and the uniqueness of a weak solution. Also, we considered a shape memory alloy problem in three dimensions. In 3-d case the regularity of a solution is not good. Hence, we proved the well-posed ness for only approximated problem. Here, we note that we also have a plan to analyze our mathematical model, numerically. Now, we do not success to get a numerical solution of a complete problem and have an algorithm for solving a kinetic equation, which is most difficult to compute in our process.
[magnetization in ferromagnetic] : By using a generalized Duhem model we propose a mathematical model for dynamics of ferromagnetic and prove the well-posedness.
|
