Research on the stability and asymptotic shapes of nonlocal nonlinear boundary value problems including unknown definite integrals

含未知定积分的非局部非线性边值问题的稳定性和渐近形状研究

• 批准号: 18540224
• 负责人: YOTSUTANI Shoji
• 金额: $ 2.58万
• 依托单位: Ryukoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2008
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540224/
• 关键词: 非線形現象; 大域的分岐構造; Cahn-Hilliard equation; 楕円関数; 完全楕円積分; 線形化固有値問題; 非局所; 非線形境界値問題; ふりこの方程式; Sturm-Liouville理論; 反応拡散方程式; Chan-Hilliard equation

微分方程式の係数の中に解自身の定積分項を含む、非局所非線形境界値問題は、物性物理学や微分幾何学等にあらわれるが、大域的解構造の解明の手法は数年前に研究代表者により突破口が開かれ、今回の研究課題遂行結果、応用範囲が拡がり、手法も深化した。従来未解明であった、Cahn-Hilliard方程式の空間1次元定常解の大域的分岐構造を完全に解明した。さらに、反応拡散方程式の定常解のまわりでの線形化固有値問題の固有値を決定する超越方程式、および、固有関数を表示する方法を発見し、その超越方程式の解析手法を示した。

In the differential equation "number", it is necessary to solve the problems of self-determination, non-local boundary problems, physical property physics, differential physics, and so on. A few years ago, the research representative opened a breakthrough, and this time, the research problem has been completed, the scope has been applied, and the technique has been deepened. In recent years, the bifurcation of the first-order steady solution of the Cahn-Hilliard equation in space has not been solved completely. The fixed solution of the equation, the inverse equation, the solution of the equation, the equation.

项目成果

Phase pattern in a Ginzburg-Landau model with a discontinuous coefficient in a ring

环中具有不连续系数的 Ginzburg-Landau 模型中的相位模式

• 发表时间: 2006
• 期刊: Discrete Conti.Dynam.Systems 14
• 作者: S.Kosugi;Y.Morita
• 通讯作者: Y.Morita

Stationary solutions to the one-dimensional Cahn-Hilliard equation: Proof by the complete elliptic integrals

• DOI: 10.3934/dcds.2007.19.609
• 发表时间: 2007-09
• 期刊: Discrete and Continuous Dynamical Systems
• 影响因子: 1.1
• 作者: S. Kosugi;Y. Morita;Shoji Yotsutani

Quantitative hyperbolicity estimates in one-dimensional dynamics

一维动力学中的定量双曲性估计

• 发表时间: 2008
• 期刊: Nonlinearity 21
• 作者: S.Day;H.Kokubu;S.Luzzatto;K.Mischaikow;H.Oka;P.Pilarczyk
• 通讯作者: P.Pilarczyk

Bifurcation analysis for a Ginzburg-Landau

Ginzburg-Landau 的分岔分析

• 发表时间: 2007
• 作者: Satoru Yamamoto;Hiroshi Kimura;Evgenij Zubko;Hiroshi Kobayashi;Koji Wada;Masateru Ishiguro;and Takafumi Matsui;Y. Morita
• 通讯作者: Y. Morita

Bifurcation of vortex and boundary-vortex solutions in a Ginzburg-Landau model

Ginzburg-Landau 模型中涡旋和边界涡旋解的分叉

• 发表时间: 2007
• 期刊: Nonlinearity Vol.20,Issue4
• 作者: S.Kosugi;Y.Morita and S.Yotsutani;C.-N.Chen and Y.Morita
• 通讯作者: C.-N.Chen and Y.Morita