Study of structures of solutions to variational problems, optimization problems and nonlinear partial differential equations

变分问题、优化问题和非线性偏微分方程解的结构研究

• 批准号: 22540203
• 负责人: KURATA Kazuhiro
• 金额: $ 2.08万
• 依托单位: Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540203/
• 关键词: 関数方程式; パターン形成; 変分問題; 非線形楕円型方程式; 特異摂動問題; 楕円型作用素の固有値; 非線形楕円型固有値問題; 逆問題; 解析学; 非線形現象

We proved existence of non-constant stationary solutions to nonlinear reaction-diffusion equations arising in some pattern formation problems, for example, an Allen-Chan modelwith non-homogeneous environment and a Chemotaxis model with saturation effect.

我们证明了一些模式形成问题中非线性反应扩散方程的非常稳态解的存在性，例如具有非均匀环境的Allen-Chan模型和具有饱和效应的趋化性模型。

项目成果

Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential

• DOI: 10.4171/jems/407
• 发表时间: 2013-07
• 期刊: Journal of the European Mathematical Society
• 影响因子: 2.6
• 作者: Jaeyoung Byeon;Kazunaga Tanaka

A local mountain pass type result for a system of nonlinear Schrödinger equations

• DOI: 10.1007/s00526-010-0347-x
• 发表时间: 2011
• 期刊: Calculus of Variations and Partial Differential Equations
• 影响因子: 2.1
• 作者: N. Ikoma;Kazunaga Tanaka

NONLINEAR SCALAR FIELD EQUATIONS IN R N : MOUNTAIN PASS AND SYMMETRIC MOUNTAIN PASS APPROACHES

• 发表时间: 2010
• 作者: Jun Hirata;N. Ikoma;Kazunaga Tanaka

Global behavior of bifurcation curves for a class of boundary value problems

一类边值问题的分岔曲线的全局行为

• 作者: K.Ishige;M.Ishiwata;T. Uehara;F.Hiai;Tetsutaro Shibata
• 通讯作者: Tetsutaro Shibata

Inverse bifurcation problems for non-autonomous semilinear Sturm-Liouville equations

非自治半线性 Sturm-Liouville 方程的反分岔问题

• 发表时间: 2012
• 作者: K Itoh;R. Sakai and N. Suzuki;T.Kobayashi;田原秀敏 & 山澤浩司;Tetsutaro Shibata
• 通讯作者: Tetsutaro Shibata