Study on the global structure of the stationary solutions of Reaction diffusion equation and its limiting system

反应扩散方程平稳解的全局结构及其极限系统研究

• 批准号: 20540122
• 负责人: TSUJIKAWA Tohru
• 金额: $ 2.33万
• 依托单位: University of Miyazaki
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540122/
• 关键词: 非線形偏微分方程式; 非平衡力学系; 反応拡散方程式; 縮約系; 分岐理論; 定常問題; 写像度; 特異摂動法; 分岐構造

From the viewpoint of pattern formations, we show the structure of stationary solutions depending on the parameter, for example, diffusion coefficients. The bifurcation theory is applicable to prove the existence of non constant solutions.To show the existence of a traveling solution corresponding to a propagating arc-like segment which is observed in the experiment of BZ reaction system with feedback, we study some kind of the limiting system to the reaction diffusion equation.

从图案形成的角度来看，我们显示的结构固定的解决方案取决于参数，例如，扩散系数。分支理论适用于证明非常数解的存在性，为了证明在BZ反应系统的反馈实验中观察到的传播弧段所对应的行波解的存在性，我们研究了反应扩散方程的一类极限系统.

项目成果

Second order numerical scheme for motion of polygonal curves with constant area speed

等面积速度折线运动的二阶数值格式

• 发表时间: 2009
• 期刊: Interfaces and Free Boundaries 11
• 作者: M.Bene\vs M.Kimura;S.Yazaki
• 通讯作者: S.Yazaki

Kinematic model of propagating arc-like segments with feed back

带反馈的弧形段传播运动模型

• 发表时间: 2008
• 期刊: Physica D 237
• 作者: T. Sakurai;K. Osaki;and T. Tsujikawa
• 通讯作者: and T. Tsujikawa

Stationary solutions of an adsorbate-induced phase transition model

吸附物诱导相变模型的稳态解

• 发表时间: 2009
• 作者: Naoko Kurata;Tatsunari Sakurai;T.Tsujikawa;Tohru Tsujikawa;矢崎成俊;T.Tsujikawa;大塚浩史;大塚浩史;矢崎成俊;T.Tsujikawa;Tohru Tsujikawa;T.Tsujikawa
• 通讯作者: T.Tsujikawa

Global structure of stationary solutions of shadow system for adsorbate-induced phase transition model

吸附质诱导相变模型阴影系统平稳解的全局结构

• 发表时间: 2008
• 作者: Kuto Kousuke;Tohru Tsujikawa;T.Tsujikawa
• 通讯作者: T.Tsujikawa

Bifurcation structure of steady states in the shadow system for the adsorbate-induced phase transition model

吸附质诱导相变模型的阴影系统稳态分岔结构

• 发表时间: 2009
• 作者: L.H.Chuan;T.Tsujikawa;Atsushi Yagi;辻川亨;Tohru Tsujikawa;永井敏隆;T.Nagai;T.Nagai;佐々木拓紀;T.Tsujikawa;T.Nagai;永井敏隆;永井敏隆;中木達幸;永井敏隆;T.Tsujikawa
• 通讯作者: T.Tsujikawa