Analysis of a non-linear phenomenon mainly on the issue of shape-memory alloy

主要针对形状记忆合金问题的非线性现象分析

• 批准号: 16540146
• 负责人: AIKI Toyohiko
• 金额: $ 2.3万
• 依托单位: Gifu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540146/
• 关键词: Shape memory alloy; Hysteresis operator; Free boundary problem; nonlinear partial differential equation; 非線形偏微分方程式; 最大正則性評価

[2004] In dynamics of shape memory alloys the relationship between the strain and the stress can not be described by a usual function and is described by the hysteresis operator. In this research project we describe the relationship by the stop operator, which is one type of hysteresis operators. Throughout the previous works we needed some largeness for the viscosity in order to establish the well-posedness of our mathematical model. In this year we can remove the assumption for the viscosity.[2005] As a reviewing process for our mathematical model for shape memory alloys, we have noticed that there were no mathematical results concerned with change of shape of elastic materials. Hence, we have proposed a mathematical for elastic materials, which is given by a free boundary problem. Here, we proved the local existence of a solution in time for the free boundary problem. In the poof the standard approximation method was used.[2006] The result of this year is to obtain the uniqueness result for our free boundary problem. In the whole research project we can not prove the global existence of a solution. We continue to study the dynamics for the elastic material.

[2004]在形状记忆合金的动力学中，应变和应力之间的关系不能用通常的函数来描述，而是用迟滞算子来描述。在本研究项目中，我们用一种迟滞算子——停止算子来描述它们之间的关系。在之前的工作中，我们需要一定的黏度来建立数学模型的适定性。今年我们可以去掉对粘度的假设。[2005]在回顾形状记忆合金数学模型的过程中，我们注意到没有涉及弹性材料形状变化的数学结果。因此，我们提出了弹性材料的一种数学方法，它是由自由边界问题给出的。在此，我们证明了自由边界问题解的局部存在性。本文采用标准逼近法。[2006]今年的结果是得到了自由边界问题的唯一性结果。在整个研究项目中，我们无法证明一个解决方案的全局存在性。我们继续研究弹性材料的动力学。

项目成果

地域経済の流れを記述する常微分方程式における係数の決定方法

如何确定描述区域经济流动的常微分方程中的系数

• 发表时间: 2006
• 期刊: 経済科学研究(広島修道大学) 第10巻第1号
• 作者: 伊藤昭夫;角谷 敦;白川 健
• 通讯作者: 白川 健

Wellposedness for a new mathematical model for magnetostrictive thin film multilayers

磁致伸缩薄膜多层新数学模型的适定性

• 发表时间: 2004
• 期刊: Advances in Mathematical Sciences and Applications Vol.14
• 作者: T.Aiki;K-H.Hoffmann;T.Okazaki
• 通讯作者: T.Okazaki

Periodic Solutions of Elliptic-Parabolic Variational Inequalities with Time-Dependent Constraints

• DOI: 10.3934/dcds.2007.19.335
• 发表时间: 2006-02
• 期刊: Journal of Evolution Equations
• 影响因子: 1.4
• 作者: M. Kubo;N. Yamazaki

A prey - predator model with hysteresis effect

具有滞后效应的捕食者模型

• 发表时间: 2005
• 期刊: SIAM Journal on Mathematical Analysis Vol.36
• 作者: T.Aiki;E.Minchev;T.Okazaki
• 通讯作者: T.Okazaki

Local solvability of a constrainted gradient system of total variation

全变分约束梯度系统的局部可解性

• 发表时间: 2004
• 期刊: Abstract and Applied Analysis Vol.9
• 作者: Y.Giga;Y.Kashima;N.Yamazaki
• 通讯作者: N.Yamazaki